The following suggestions are dangerous and should be avoided at all costs. Anyone not in the position of this poster shouldn't even think about these...
First, get a very high gauge needle. 31g preferably, definitely no larger than 30g. The following spots are hittable with a very small needle: the joints between segments of your fingers, veins in the palms of your hand, veins near your ankles, many smaller veins in the hands that aren't possible to access with a large needle.
These all collapse extremely quickly, sometimes permanently after a single use.