well, that's the way it goes with DADGAD. As a DADGAD enthusiast who likes to sing in C, I can only say that they're not compatible in any normal way. (although capo on 10th fret is possible, if you don't mind the high tinkly sound and limited range on the fretboard. It's more for "special effect" sound--like an imitation modal autoharp than the customary big, wide, midrange DADGAD palette. B flat though, you can do, and A (7th fret) is common--and a very good singing key for many songs.

Now, if you have a guitar that can be dropped without sounding flabby, you can tune the DADGAD down to CGCFGC for true DADGAD in C. Using medium strings and patience this can work alright. Martin Carthy does something similar, but in a tuning somewhat more dissonant than DADGAD, (DADEAB > CGCDGA) which can become cloyingly pretty after awhile.

The Stan Rogers Songbook (OFC Publication) has excellent DADGAD chord and lots of nice variations on the more comon inversions. That's where I learned to use the tuning from.

Willie-O