A tetraquark is four quarks. There exist three -1/3e quarks (dsb), three +2/3e quarks (uct), and then their +1/3e and -2/3e antimatter counterparts. 1e is the charge of one electron. The stability of a tetraquark is mainly a color/strong force thing and the electric charge comes along for the ride. Stable atomic nuclei, which are held together by the strong force, go up to +83e and they still don't fall apart due to electric repulsion.
However, there is one constraint that might show up in charge. Tetraquarks always have two antiquarks, which is necessary for the color charge to come out to zero. Working out every possible combination is left as an exercise for the reader. :)
The highest possible charge is 2/3 + 2/3 + 1/3 + 1/3 = 2. Every swap of a quark to a lower charge one reduces the total charge by 1. So the possibilities are 2, 1, 0, -1, -2.
However, there is one constraint that might show up in charge. Tetraquarks always have two antiquarks, which is necessary for the color charge to come out to zero. Working out every possible combination is left as an exercise for the reader. :)