Shortly after Jim's death, Nick had a "Sunday Night Muppets" block... while I don't know for sure if TMS was part of that block (I'm assuming it was), I know for a fact they also aired holiday specials, because I have recordings of THE MUPPETS' VALENTINE SHOW and THE CHRISTMAS TOY from Sunday Night Muppets.
The Sunday Night Muppets block happened in November and December 1992, and featured (in order from the best I can remember) The Frog Prince, The Muppets Go to the Movies, The Muppet Musicians of Bremen, The Secrets of the Muppets, The Christmas Toy, A Muppet Family Christmas, and Emmet Otter's Jug-Band Christmas (so every other special was basically a story special with very few recognizable characters, alternating with a "Muppet Show Special"). The following year, again from November until December, Nick ran "Friday Night Muppets", with the same specials in the same order (except I specifically don't remember The Frog Prince being included; maybe it was and I just missed the commercials and didn't watch Nickelodeon that Friday night).
I wonder why they ended after only two months, since Nickelodeon clearly had the broadcast rights to more specials (though I wonder if Nick might have obtained the rights to more later on, in time for Muppet Matinee). Some of the specials would air as part of Special Delivery, and on Memorial Day 1993, Nick aired an 8-hour Muppet marathon, with each hour alternating between a special and two back-to-back episodes of Muppet Babies, but most of the specials were the same ones shown on Sunday Night Muppets, the only exception being Hey Cinderella (I wonder if that one was ever shown as part of Special Delivery... I wouldn't start looking in the TV listings every week until Muppet Matinee began, but I wouldn't be surprised if before I looked in the listings and saw Hey Cinderella, Living with Dinosaurs, Monster Maker, or Tale of the Bunny Picnic in the Special Delivery time slot and didn't care because the titles don't have anything Muppet-related in them).
But the Muppets were never on Nick at Nite, though Sunday Night Muppets and The Muppet Show were right before Nick at Nite, as was the first Nickelodeon broadcast of The Muppets Valentine Show. I have Nickelodeon recordings of TMS episodes that have the "coming up next on Nickelodeon..." bumper before that (and not announcing anything after, which was the case with the shows that came before Nick at Nite), and I'm pretty sure I have a few that continue recording right to the start of Nick at Nite (where a special bumper telling us that Nick at Nite is starting is played).