$NP\cap coAM$ Languages
The only other ones I know of are also isomorphism problems: group isomorphism and ring isomorphism.  The $coAM$ protocols for both of these are essentially the same as for graph isomorphism.

Group isomorphism reduces to graph isomorphism reduces to ring isomorphism.

Interestingly, unlike (what is known for) groups and graphs, for rings, determining whether a ring has a nontrivial automorphism is in $P$, while finding a nontrivial automorphism is equivalent to factoring integers.  See Neeraj Kayal, Nitin Saxena. Complexity of Ring Morphism Problems. Computational Complexity 15(4): 342-390 (2006).