Just exactly how small is his small frame?

The .243 is an excelent deer cartridge with the correct bullets. It shoots fast and flat so it can be sighted in so he won't have to worry about holding over the deer or anything like that.

The 30-30 is another great deer cartridge for a first time hunter. So is the .257 Roberts, 7mm-08, 260 Rem, 6mm Rem.

Still another option is letting him use the 30-06 until his dad can get him his won rifle. Get him sighted in and practicing with the Remington managed recoil loads. These kick about like a .243 and have plenty of umph at 250 yards for deer.