If wanting a shallow Rd. hole similar to a T/Cs patch box. The proper drill bit for the job is called: Forstner Bit. But it's best used in a drill press with a jig set-up to help center your stock under the bit. Or someone with a awfully steady but strong arm & hand perhaps can get by in drilling free handed. (not the prefered way) I think their available for purchase from Lowe's, Home Depot or perhaps Harbor Freight.
"JUST A OLD DEPLORABLE THAT'S IRREDEMABLE."