Hello Eaglejonny,
May as well turn the "firehose" on full, so long as you've asked the question about image erectors for telescopes. Lots of alternatives here to consider:
1. The simplest "image erector" if you happen to choose a Newtonian (sometimes called Dobsonian because of its mount) reflecting telescope is simply to aim the big tube horizontal (or in your case, slightly downhill) at the nest and stand with your back to the nest as you view and look "down" into the eyepiece projecting from the top side of the scope tube. Obviously you cannot stand in front of the scope, since that would block the light. It is pretty easy to stand a little to one side and get a nice, erect and correct right-and-left image view. I have a friend who uses a 10" diameter scope like this to watch grizzly bears.
2. If you use a refractor astro scope "straight through" the image will be upside down, so you need to somehow invert the image so up-down is correct and MAY also want to revert the image, correcting so right and left are properly oriented. A commercially available 1.25" or 2" aperture "diagonal" mirror or prism will accomplish the "invert" function and is the most cost effective way to go with a refractor. The eagle in the scope image will be facing the opposite way, left and right, but will be upright. Some folks do not mind this, others do. Right angle diagonals simply slip into the scope focuser tube and the eyepiece used is then inserted into the diagonal to view at right angles.
3. if you want a fully "correct" image with a refractor, there are several good options, but none are particularly simple or cheap.
a. A straight-through (with offset) Porro prism cluster can be purchased that will fit in a 1.25" focuser tube and hold the eyepiece for "correct viewing". This is a good solution, but requires the telescope to have a long travel focuser to allow enough "in" travel to accommodate the optical path length of the Porro prism pair cluster to reach infinity focus with your eyepiece. I've made scopes that use this prism scheme with a surplus 7 x 50 binocular Porro prism cluster ($15 or so) built within the homemade main scope tube. There is also a Porro Type 2 prism that does the same thing, but is arranged differently for easier use in a homemade spotting scope. See this archived thread from Cloudy Nights site for a 2" diameter Porro Type 2 prism cemented up using two Porro-Abbe prisms. This type can also be cemented up from 4 identical common right angle prisms. https://www.cloudynights.com/topic/185367-surplus-shed-127700mm-rftspotter/#entry2391788
Many commercial spotters use Porro prisms with the two prism sets separated so that moving the prisms apart and together changes focus..
b. Sometimes, the Porro prism erecting system is followed by a "half penta prism" that serves to change the viewing angle to 45˚. Pentax PF spotters use this scheme. It works well, but cuts into edge of field illumination for close viewing distances.
c. A separate 45˚ prism can slip into the refractor focuser and give a fully corrected image. These are Schmidt prisms and are in the category of "roof prism" design. The "roof" is simply a right angle reflective portion of the back of the prism where light on the left is reflected right and right to left by total internal reflection. Schmidt prisms are sometimes incorrectly called Amici prisms.
d. An Amici prism is a right angle roof prism that again gives a fully corrected image, but is viewable by looking at 90˚ from the telescope axis. The Amici prism is commercially available in both 1.25" and 2" focal tube diameters and can slip into the telescope focuser tube and will hold different eyepieces for viewing. Like the Porro prism cluster and Schmidt prism, the Amici prism requires more "in" focuser travel than straight through "inverted" viewing, but needs less "in" travel than the insertable Porro or Schmidt prism erectors.
e. The Schmidt-Pechan prism is common in roof prism binoculars and some other prism types are occasionally utilized (Leitz Trinovid), but those are rarely seen in refractor erecting systems.
Hope this at least gives you a starting point in your research as to what optics are usable for your eagle viewing. Your nest should provide fascinating views.
May as well turn the "firehose" on full, so long as you've asked the question about image erectors for telescopes. Lots of alternatives here to consider:
1. The simplest "image erector" if you happen to choose a Newtonian (sometimes called Dobsonian because of its mount) reflecting telescope is simply to aim the big tube horizontal (or in your case, slightly downhill) at the nest and stand with your back to the nest as you view and look "down" into the eyepiece projecting from the top side of the scope tube. Obviously you cannot stand in front of the scope, since that would block the light. It is pretty easy to stand a little to one side and get a nice, erect and correct right-and-left image view. I have a friend who uses a 10" diameter scope like this to watch grizzly bears.
2. If you use a refractor astro scope "straight through" the image will be upside down, so you need to somehow invert the image so up-down is correct and MAY also want to revert the image, correcting so right and left are properly oriented. A commercially available 1.25" or 2" aperture "diagonal" mirror or prism will accomplish the "invert" function and is the most cost effective way to go with a refractor. The eagle in the scope image will be facing the opposite way, left and right, but will be upright. Some folks do not mind this, others do. Right angle diagonals simply slip into the scope focuser tube and the eyepiece used is then inserted into the diagonal to view at right angles.
3. if you want a fully "correct" image with a refractor, there are several good options, but none are particularly simple or cheap.
a. A straight-through (with offset) Porro prism cluster can be purchased that will fit in a 1.25" focuser tube and hold the eyepiece for "correct viewing". This is a good solution, but requires the telescope to have a long travel focuser to allow enough "in" travel to accommodate the optical path length of the Porro prism pair cluster to reach infinity focus with your eyepiece. I've made scopes that use this prism scheme with a surplus 7 x 50 binocular Porro prism cluster ($15 or so) built within the homemade main scope tube. There is also a Porro Type 2 prism that does the same thing, but is arranged differently for easier use in a homemade spotting scope. See this archived thread from Cloudy Nights site for a 2" diameter Porro Type 2 prism cemented up using two Porro-Abbe prisms. This type can also be cemented up from 4 identical common right angle prisms. https://www.cloudynights.com/topic/185367-surplus-shed-127700mm-rftspotter/#entry2391788
Many commercial spotters use Porro prisms with the two prism sets separated so that moving the prisms apart and together changes focus..
b. Sometimes, the Porro prism erecting system is followed by a "half penta prism" that serves to change the viewing angle to 45˚. Pentax PF spotters use this scheme. It works well, but cuts into edge of field illumination for close viewing distances.
c. A separate 45˚ prism can slip into the refractor focuser and give a fully corrected image. These are Schmidt prisms and are in the category of "roof prism" design. The "roof" is simply a right angle reflective portion of the back of the prism where light on the left is reflected right and right to left by total internal reflection. Schmidt prisms are sometimes incorrectly called Amici prisms.
d. An Amici prism is a right angle roof prism that again gives a fully corrected image, but is viewable by looking at 90˚ from the telescope axis. The Amici prism is commercially available in both 1.25" and 2" focal tube diameters and can slip into the telescope focuser tube and will hold different eyepieces for viewing. Like the Porro prism cluster and Schmidt prism, the Amici prism requires more "in" focuser travel than straight through "inverted" viewing, but needs less "in" travel than the insertable Porro or Schmidt prism erectors.
e. The Schmidt-Pechan prism is common in roof prism binoculars and some other prism types are occasionally utilized (Leitz Trinovid), but those are rarely seen in refractor erecting systems.
Hope this at least gives you a starting point in your research as to what optics are usable for your eagle viewing. Your nest should provide fascinating views.