Further - I assume the 1137 are OK for lower pressure BP loads, however, I would want proper 4140 or 5140 for Nitro-express barrels.
I would call Green Mountain for Nitro barrels.

www.tackofthewolf.com has or used to have some GM barrels, .44 up to .50 cal. for Winchester's & Sharps etc. I am using just such a barrel on my Sharps. Be careful of the rifling twist as they have some of the slow Winchester twists of the 1880's. The barrel I bought is a #3 or 3 1/2 heavy Winchester taper, 18" twist & 35" long. It gets 405gr. at 1,850fps in the 1.9", .45/60 chambering, and producing only about 22,000PSI (.45/70 data at 2.55" oal) using Benchmark powder. I used my .458 2" reamer to chamber it, stopping when the belt portion of the reamer cut full depth. I only had to enlarge that cut-tout to fit the .604" rim of the shortened.45/70 case. This barrel put 10 of those bullets into a 7/8", C to C group off the bags at 100 meters for me. I pulled the 9th out of the group, so had to fire 11 to get the 10 shot, 7/8" group. The rifle had a Sharps globe front sight and a decent aperture tang sight as well, this one. http://www.trackofthewolf.com/Categories/PartDetail.aspx/883/2/RS-DP-SOULE-4

http://www.trackofthewolf.com/List/Item.aspx/643/1 barrel page