Red Squirrels can be seen in Camperdown Park in Dundee without too much trouble (there are feeders by the countryside rangers office at the back of Camperdown House). There is also a small Wildlife Centre (zoo) in the park, so for a less 'birdy' day out with your cousin you could possibly combine a visit to the park with your search for Squirrels?
http://www.camperdownwildlifecentre.com/visitor-information/how-get-here
Another place to see them relatively easily and only a short bus journey and walk from Dundee is Morton Lochs, just outside Tayport (it is possible to walk across the golf course to the reserve. PM me for details if you like). The Tay at Tayport can be good for waders and seaducks, though dependent on tide times they can be quite distant. Morton Lochs has a selection of ducks, Little Grebes, Kingfishers, Herons and tits, finches, woodpeckers etc in addition to the Red Squirrels.
Ordinarily I'd suggest Guardbridge for more birds but there are major roadworks happening until some time in April that complicates the bus journeys a bit too much (tried it today). All really depends what species you hope to see, and how much time you have available (early start etc).
Another possibility would be to contact Stuart Green at Angus Birdtours and arrange a guided day out. Stuart certainly knows his stuff and you'd have the transport aspect covered and have a very good chance of seeing a good variety of species. Obviously this would be a more expensive way of doing things but your chances of a successful day out would be greatly enhanced.
http://www.angusbirdtours.com/
Within an hour of Dundee you have a chance of seeing species as diverse as Hawfinch, Bearded Tits, White Tailed Eagle, Puffins, Ravens and countless others. It is best to have a contingency plan for your Isle of May day as the boat doesn't sail if it is too windy.