There are lots. J-3 Cubs, of course, though Cubs are slower (and more expensive!) than almost any other aircraft of that vintage. All B model Taylorcrafts. Aeronca Champ, probably Interstate Kadet, Porterfield, many others. Cessna 120, I think (but not the 140). Some models of Ercoupe (later ones, like the C-140, have too high gross weight). Later Lucsombes are too heavy, too. The rag and tube planes like the Cubs, T-Craft, and Champs are probably easier to repair than the all metal planes. There's a wing strut AD on the T-Craft and I think there's something on the Luscombes, too.

Note that you can't reduce the gross weight of an aircraft to meet the LSA specs; if it was ever certificated at a higher gross weight then it's permanently ineligible for LSA.