Scope mounting question

I have a Rossi .22/410 combo for my daughter. I had a red dot on it with a weaver base made for the Rossi. I just picked up a clearance scope from Wal-mart. It has the thinner mounting rings\base like what you see for air rifles and some .22's. These ring bases are too small for the weaver rail, and I looked at scope rings and the tube portions all seem too big for this scope.

Do they make a unit that mounts on a weaver rail but has the smaller mounting rail like what you see on the air guns and .22's? OR, do they make rings with a smaller diameter that will fit a weaver rail?

Here is the scope http://www.opticsplanet.net/bsa-rimfire-3-7x20-riflescopes-clam-pack.html

Wally World had it on clearance for $8.

Thanks in advance for any help you can provide!