Techniques for showing that problem is in hardness "limbo"
Showing that your problem is in coAM (or SZK) is indeed one of the main ways to adduce evidence for "hardness limbo."  But besides that, there are several others:


Show that your problem is in NP &cap; coNP.  (Example: Factoring.)
Show that your problem is solvable in quasipolynomial time.  (Examples: VC dimension, approximating free games.)
Show that your problem is no harder than inverting one-way functions or solving NP on average.  (Examples: Lots of problems in cryptography.)
Show that your problem reduces to (e.g.) Unique Games or Small-Set Expansion.
Show that your problem is in BQP.  (Example: Factoring, though of course that's also in NP &cap; coNP.)
Rule out large classes of NP-completeness reductions.  (Example: The Circuit Minimization Problem, studied by Kabanets and Cai.)


I'm sure there are others that I'm forgetting.