Nice looking rifle Keith. Makes me jealous!
I can only think of a few off the top of my head.
Ruger made 2 different .44 carbines. The original .44 looked almost exactly like a 10/22 but slightly beefed up. I belive it used a 4 round rotary mag akin to the 10 round rotary mag used by the 10/22. Many people that I talk with consider this Ruger .44 to be the better of the two.
The second version of the .44 carbine that Ruger made was the "Deefield Carbine" which is basically a M1 carbine chambered in .44. It uses the same rotary bolt design as the Mini-14, M1 Carbine, M1 Garand, M-14.
Ruger also made a 77/44. I saw on in the used gun rack down here at Cabelas and played with it. I really felt like walking away with it, except for the $500 price tag. I don't think ruger makes this model anymore, but it sure was nice looking. I would guess it had a 18-20inch barrel.
Rossi makes the Model 92 lever action in .44. I have never handled or shot a Rossi so I can't comment on the quality.
Puma also makes a Model 92 chambered in .44. Like the Rossi I can't comment on this one. I haven't even seen a puma in real life before.
Hope this helps.