.32-40 was only ever chambered in the 1893 series.
So any 1893, 1936, 36, 336, 30A, 30AS, etc. should be capable of accepting the barrel.
The standard bolt face (.30-30, .219 Zipper, .307 Win, .444 Marlin, etc.) would, of course, make things easier.
*Also compatible:
-The Model 444 with standard, .30-30-style cartridge lifter (no set screw on left, forward face of receiver).
-Glenfield 30, 30A, 35, 36, 36G, etc.
-Western Field, Western Auto, Sears, JC Penney, Firestone, and other 'store brand' models.