For SU2 and even SU2(q) the triangle condition is, well, the triangle condition (conveniently, all irreps are described by (half)integer J completely). Additionally, all three J of a triple must add to integer.
But what is the analogue to that for some arbitrary (quantum) group? As usual, I don't have a clue but an assumption :-) - random example in group A3: Let the reps be 1R1+2R2+1R3,2R1+R2+1R3 and 5R1+2R2+2R3, then you check every irrep separately: 125 - triangle fail, 212 - parity fail, 112 - pass, overall: fail.
Of course, I could be totally wrong...What is the correct condition? (Maybe it's not even a simple one: outer multiplicity and that.)