There is, of course, no perfect solution or we wouldn't have all the options =)
You CAN print on dark shirts with transfer paper (requires a special 'opaque' kind), but personally I wouldn't recommend it as the quality is low.
Besides screen printing, your options for dark shirts include Direct-to-Garment printing (also quite expensive, but may come down in the next few years), Plastisol transfers (runs as low as 12 can be reasonably priced for 1-color, and you can often gang up multiple designs on one sheet), and Vinyl (you will, of course, need a cutter; a good new one will run you $1200+, but this is your only quality option of small runs on dark shirts besides
DTG).
You might call around to see if you can find a used cutter somewhere local for a decent price; local is good because it saves on shipping and you can check it out before you buy it. Try sign shops, t-shirt shops, etc.