Well, it was obvious in a couple of the piano sketches that Rowlf and Piggy have a good working friendship based on their mutual talent. Rowlf was a big appreciator of women in general, and when Piggy was bringing home a torch song, Rowlf was happy witness it. Also, I always felt there was a sort of musicians meeting-of-the-minds with Rowlf and the Mayhem. Again, mutual respect and talent.
I second that. At least show wise, Rowlf seemed to be paired up with Fozzie, Piggy, and the Mayhem a lot. As Aunt Ru mentioned, many of Piggy's torch songs and piano pieces were always done by Rowlf, while he and Fozzie seemed to have a good relationship which I think works personality wise.
I always thought that he and Dr. Teeth would be pretty tight, being pianist and all, and obviously I think Rowlf, Piggy, and Janice get along well cause of their Vet's Hospital sketches. In fact, many of the jazz standards were usually done with Rolwf playing piano, which of course is interesting as, technically Dr. Teeth does play piano; I mean, a keyboard is just a electric/portable version of one.
But with that said, I think you'll find that every author has their own preference in regards to characters and friendship - for example, I think Piggy and Floyd (and Gonzo) have a frienemy relationship with each other. No proof, I just happen to like that idea.