Well... Given the scenario in the opening sequence of TMM... Would there be swamplands and alligators in Missouri?
Besides, the gang goes back to what Kermit calls his native home in a 1989/1990 TV special... Where the gang gets startled by a fireworks show nearby... Which is the regular nightly fireworks show at Walt Disney World, cause it's next to the swamps.
Given all of that, I think it's safe to say that Kermit's home swamplands is the Everglades in the state of Florida. However, fanfics by the Queen from Chicago have placed that birthing bogg in the town of Leland, Mississippi as a nod to Jim's birthplace of Oxford, Mississippi.
Hope this helps.