My first choice for a kid would be the Single Six convertible or a Single ten. Second choice would be an SP101 22 LR. I bet you could find a used one for <$500. Put a set of Hogue grips on it and he's good to go.
NRA LIFE MEMBER GOD BLESS OUR TROOPS ESPECIALLY THE SNIPERS! "Suppose you were an idiot And suppose you were a member of Congress... But I repeat myself." -Mark Twain