Those are good ides! But here are some other good ides Birdzilla from Winnie the Pooh, The Titans from Hercules, Herbert Landon when he got turend into a mutant monster, The Sentinels from X-Men.
Herbert Landon and the Sentinels (as well as the Tri-Sentinal, IF he appeared in a cartoon) would make pretty good opponents! Birdzilla though, I believe I'll leave out since he's a gag character from a show within a show. The Titans, I've CONTEMPLATED on doing, but because they're so gargantuan compared to Godzilla (The Stone Titan's Foot can crush en entire city, and the Wind Titan's a Tornado,) I had to drop them. However, I could have the Big G fight the Cyclops since he's decently sized enough to pair him against Godzilla.
Looks like a tie between the stone jaguar, Mo Mojo (Giant Mojo Jojo's monster name) & Koopzilla