Check out Arkia - they fly to a number of places in Europe. I flew them 3 weeks ago from TLV to Larnaca. Stayed a few days there and then crossed into N. Cyprus and flew out of ECN to IST on TK.

I don't know if this will work if you try doing it the other direction unless you have an EU passport as you may run into problems when trying to leave via LCA since you won't have an entry stamp into Cyprus when crossing the green line.