Funny, I was going to post a question about cork tiles today and saw your post. I have a room with cork tiles that we put down about 12 years ago. Obviously I must have had little to do with my time then, and I drew a pattern on the floor and filled it in with a dark woodstain, and then put down about 3 coats of varnish. If I say so myself, it looked pretty good! So I would suggest you find a shade of woodstain you like and work away on unfiinished tiles and then varnish them.
Now my question - maybe someone might help - is there anything I can do to revive my cork floor? It has got very worn at this stage and I doubt it can be sanded but would give it a go if I thought it wouldn't wreck the cork altogether.