Is there any source for Stevens 1894 replacement barrels?  I have been looking with no luck.  If I had only the usual problem (shot out or corroded barrel), this would probably be simpler; get the original relined.  My bore is typically bad, but, it looks like the barrel was refinished once before.  The barrel is half octagon, half round.  When the barrel refinish was done, the flats on the octagon end were not carefully refinished and the flats at the receiver end are rounded off.

Danny

Gun Parts Corp. has new replacement favorite barrels for the 1915 favorites at $133.59 part #593550. If I am remembering correctly the barrel shank on a 1915 favorite is slightly longer than a 1894 favorite so quite a bit of extra fitting would be needed to use one of these barrels.  These replacement barrels have 3/8" sight dovetails so the original sights will not fit. The original forearm will not fit either because these barrels while being part octagon they are not milled round on the bottom like the original barrels are.
I would watch ebay for a original 1894 barrel in better condition than your original barrel as they show up often on ebay. You would likely still need to put a liner in it, as favorite barrels with good bores are scarcer than hens teeth. Perhaps someone on this site might have a suitable 1894 barrel they would sell.

would a Varner 1895 barrel work?
I have a Varner barrel I could measure if you would like.

this is a sketch of a Varner barrel I fitted to a Stevens Favorite, it would not group at 25 yards, come to find out the barrel is bent
Had to resize the photo, so hope you can see it

Right now, looking on Gunbroker and eBay for a used example with a good exterior, needing liner might be the best solution.  Trying to get one made could come later.  I would try to do it on my own, but turning the long tapered section is beyond what I have ever tried or am set up to do.  Turning and milling on the breech end: not a problem.

Danny

I did that once.  Lots easier than drilling out a .22 barrel, which I have also done.  Put a 1" long sleeve in the breech end before reaming to take care of the crude .32 S&W chamber & rim recess that Milo Parkenfarker had done.  

.32 barrels are thin on the ground, though. 

I have a 'complete' Favorite I'm planning on selling. Pretty sure its a '94, half octagon. Sloppy loose, chip out of the forearm, needs a liner...

Barrel is good outside, nice brown patina on it. Not sure if I have an 'inventory' list on my shop pc in CA,  but I'll be back in TX Tuesday eve to double check and get pictures if you're interested. Probably sell it shipped for somewhere around the cost of a new barrel.

I just removed a 25 barrel from a Favorite.  Very nice on the outside bore might be shootable, definitely could be lined.  6 o’clock extractor.  Also have good wood, buttplate.  I’m keeping the sights.   
I’ve put liners in probably half dozen or more barrel so I could probably do it but, not sure I want to get into that and would need your action besides.
Bob