My youngest asked for piano lessons at 3. He went for about 6 months for 20 minute lessons, but the teacher asked us to stop because his hands were too small and he was having trouble with holding his hands in the correct position while pushing down the keys. He could pick out songs with two fingers but not play correctly.

I'd personally to do "Sure, honey, we'll look into it..." and then drop it unless he continues to beg. I wouldn't recommend guitar that young for the coordination, size issues.