Darhon Rees-Rohrbacher (http://www.dragonflower.com/homepage.html) says this:
Actually, you can easily adapt music in flat keys for a harp tuned in C. For the Eb pieces, just play them in 4 sharps instead – key of E major. Play on the same strings as originally notated and the piece will sound fine. If there is a notation to fix a natural accidental (such as B-nat, play it as B# instead. Key of Bb can be played in key of B with 5 sharps.
My favored key for tuning for my students is the key of F, which only has the Bb in it. This opens up a whole world of music to them but still allows them to play mostly in sharp keys. You might consider that as a compromise…..and then do what I suggested for the keys of Eb and Bb.
Mary adds: I like tuning in F, as well. But I have 2 Carolan tunes I love to play in Eb, so I keep my harp tuned in 3 flats specifically to play those tunes. Also, Angi Bemiss has over 120 titles in Eb, so it is not difficult to find music. The other reason I keep my harp tuned in Eb is just in case Ray Pool is close by. Now that is another story altogether….