Not that I've seen, but that inspired me to look into it.
''Barney furries'' seems to reference instead an episode about taking care of pets under the title "Our Furry Feathered Fishy Friends". Barney Anthro however... there's not much, but there's enough Barney Porn to go around. A guy named Herpy that apparently does dinosaur porn has an image for Barney as well, but the other stuff's pretty weird too.
Muppets... I wouldn't think it'd add up to anything. I mean come on, it's puppets. Apparently Wikifur however claims otherwise:
Many of today’s pawpeteers owe inspiration to the Muppets while growing up. Shows like Muppet Babies have proven popular with babyfurs. Jim Henson was also once quoted as saying that Kermit the Frog, the very first Muppet, first appearing in 1955, and the signature character of The Jim Henson Company, was often portrayed as a representation of him and his attitude. Indeed Kermit's job on the Muppet Show is much like Henson’s: "trying to get a bunch of crazies to actually get the job done." Many furries attribute this claim to be Kermit being Henson’s fursona.
At most I'd imagine figures like Jim Henson and Kevin Clash playing somewhat into the mixed territory of furries and ventriloquism (what a frightening thought, based on my views on ventriloquists and what I've read of some on forums), but from the looks of things even Furries appear to have their limits. Muppet Furaffinity and Muppet Anthro came out with no related results, Muppet Furry seems to tangent instead into the creepy world of ventriloquism (The Puppet Workshop and MANY OTHERS), and while Muppet Porn mostly links to jokes made with toys (mostly...), Ms. Piggy seems to be a niche of her own. Work from some clay artist seems to come up a fair amount, but there's a lot of drawn stuff as well.
So, to answer in short: No, there don't seem to be any muppet/barney furries, but there's definitely people out there that find them attractive. This spans across pretty much any anthro (and sometimes not anthro) thing that you can think of.