Your shotgun has no serial number because it was made before the requirements of the 1968 Gun Control Act went into effect. This design was patented and went into production in 1913. The J. Stevens Arms & Tool Co. name was changed to J. Stevens Arms Co. in 1916, so which name appears on your shotgun gives you a little more information. Savage Arms bought Stevens in 1920, but this did not result in any changes to the markings on Stevens firearms.
Decorations on the stock suggest immediate post WW II production; they first appeared in post war sales catalogue images but were no longer shown in 1960's catalogues. No competent records exist on your firearm and it has limited collector value.
The hunter and rabbits don't hurt the value. On the other hand.....if you screw up the refinish, it could. It is still a 100 to 150 dollar single shot .410 either way.
I think the rabbits are cool, and they are still great rabbit guns. Too bad the shells are so expensive.
Thanks for all the info. It's pretty much what I expected. I have no intention of selling the gun. I purchased it for my wife and grandson. I doubt I will "screw up" the finish, I have custom made and finished many stocks in my life, I pretty much wanted to verofy it wasn't some special edition I didn't know of. Thanks for the help both of you and Happy New Year!