Kristoffer:
Cleaning can be done without any fear of scratching coatings. Many methods have been described on the forum. The way I clean is the same way that Leif described cleaning (where is Leif nowadays, anyway?).
I have NEVER used a lens pen, microfiber cloth, or lens tissue. I use cotton balls that you buy from any pharmacy. I never apply any pressure to a ball when it is in contact with a lens. Instead I use it like a tiny mop.
I use lens cleaning solution made for eyeglasses, which you can also buy at a pharmacy or discount store. A few years ago I bought some large bottles at a discount place, and when I mentioned it in a thread, one or two posters went on about how the cheap stuff would destroy coatings forever. The truth is that it is merely a wetting agent and is removed before the cleaning process is completed.
I also use distilled water, and occasionally 99% Isopropyl Alcohol (not the 94% or 97% that you buy at a grocery; 99% is available at a pharmacy).
I tear apart cotton balls as I use them, using only a third to a half of one at a time.
I start by wetting a piece of cotton with lens cleaning solution and wiping it gently over the lens. Do not apply any pressure against the lens. Again, use the cotton as if it is a tiny mop. I repeat this several times. I then do the same using distilled water, and then use dry cotton, repeating until the swirls of water haze evaporate cleanly.
Two flaws may remain at this point: (1) a tiny spot of tree sap or hardened organic liquid, which sometimes falls from the leaves of deciduous trees, or (2) swirls that don't go away. The spot can almost always be removed with the alcohol. At least in my experience every such spot has come off with alcohol. I use the alcohol the exact same way, with cotton. It will not hurt any modern coatings, though it and other solutions may be harmful to coatings on some vintage binoculars. After using the alchohol, you have to repeat the process with lens cleaning solution and distilled water.
Swirls generally mean that the lens is still not clean, so you repeat the process until you succeed.
You need to be patient and take your time. But you will not hurt your lenses.
Some other possibilities. On a few occasions my bins have gotten terribly dirty in a dust storm. I rinsed the (waterproof) bodies under slowly running water and poured tap water from my cupped hand over the lenses several times, shook them off, wiped off the bodies, and then proceeded to clean the lenses as above.
I clean lenses as infrequently as I can get away with, but as often as necessary. Even moderately dirty oculars can reduce contrast and resolution, and the smaller the exit pupil, the more the dirt affects your view.
I have cleaned all my lenses this way for years. If I examine their surfaces in open sunlight with a 10X magnifier, I still cannot find the tiniest scratch or cleaning mark on them. They are virtually perfect.
I cringe when I see people using microfiber cloths, dragging grit around on the surfaces of their lenses. And I usually go slack-jawed when I see people use their breath and t-shirts to clean lenses. I know two birders who do this to their Ultravids.