Umm, it he likes the Ditson, but wants a flat-back style, he might like a Martin Style A. Martin mandolins are relatively affordable, and some Ditsons were actually made by Martin (using the Ditson label).

The Martin mando's are considered "folk" not bluegrass style. They are not terribly loud, but have a nice sustain rather than a punchy bluegrass sound. Good for Celtic tunes. And older ones are relatively affordable, as vintage Martin anythings go.

Round soundhole rather than F-style for that extra-sustain sound.
Old Gibson A's are available too, and one of these days I'm definitely going to get one.

As noted, it depends a lot what continent you are on! If it's North America, there are a lot of old Gibsons and Martins around.

W-O