Trisha,
Check your local library for a copy of Thomas Swearengen's _The World's Fighting Shotguns_. If they don't have it, see if they can get it for you via interlibrary loan. It'll be worth the trouble, unless you have a rapidly approaching deadline to meet.
Ithaca was in the double barrel business at the time you mention. Pump shotguns were making inroads into the market for doubles, and that's what led Ithaca to look for a pumpgun design of their own in the mid-1930s. Double barrels were popular fighting shotguns from the Civil War muzzle-loader era on to modern times.
But Ithaca was doing a few interesting things in the world of fighting shotguns in the 1920s. They began marketing a pistol- gripped 10.1" barreled 20 ga. double known as the Auto and Burglar Gun. You can see a pic of a Model B Auto- Burglar Gun from about 1925 or so at
http://www.securityarms.com/20010315/galleryfiles/2800/2885.htm . The Model A had a spur at the top of the pistol grip and was less manageable to fire.
When the gun came out, apparently the first sales were to banks in the Chicago area, to equip their guards. As word spread more of the abbreviated shotguns were ordered by police and sheriffs' departments, paymasters, express messengers and other guards. A number were purchased by private citizens also. Until the National Firearms Act (NFA) of 1934 outlawed them. About 4,500 Auto and Burglar guns were built by Ithaca between 1922 and 1934.
If you need or want to use a magazine repeater to arm your character, you can start as far back as the Browning- designed Winchester Model 1887 lever action shotgun. You might recall that one of these in sawed-off configuration showed up in the hands of The Terminator in one of those movies- the first one, I think. They were made in 10 ga. as well as 12 ga., you can see a couple of pics of the 10 ga. Model 1887 recovered from Clyde Barrow at
http://texashideout.tripod.com/guns.html . There are other pictures of criminal as well as LEO weapons at this site that might be useful for you, like the sawed off Remington Model 11s (same basic design as the Browning Auto-5, produced by Remington starting in 1911) that both Bonnie and Clyde liked. Bonnie preferred a 20 ga. BTW.
The Winchester 1897 and Model 12 have been mentioned already and should be easy to find on the web. Note that both these guns were popular among lawmen as well as bandits, that some were equipped early along with extended magazines holding up to 10 or 11 rounds, and that both could be had in take-down versions that reduced their length when disassembled to half their normal size, with a shortened barrel. That made them easy to pack in a blanket roll or carpetbag.
If you want an oddity, I suggest you look at the Burgess Police Gun. You can see a pic about 4/5 of the way down the page at
http://guns.connect.fi/gow/QA18.html . This gun functioned by pumping the pistol grip/trigger guard to the rear and back, not the fore-end as with more usual pump gun designs. There was a holster that allowed it to be carried folded under a coat. There is very little information on the Burgess gun out there, as I said if you want to arm your character with an oddity this is definitely it as far as pump guns are concerned. It is of the correct time frame for you as well, if a bit old. It was first marketed in 1894, Burgess sold his company to Winchester in 1899.
Note that this web site is intended to supply answers to gun questions to writers, it may be of more help to you in other areas as well.
There are a LOT more possibilities from the time period you mention, if you narrow down your interest some more I will be happy to help further. I have a copy of Swearengen's book at hand.
Regards,
lpl/nc (retired reference librarian among other things)