Let S be a set of primes. We call an m-tuple (a1,… ,am) of distinct, positive integers S-Diophantine, if for all i≠ j the integers si,j:=aiaj+1 have only prime divisors coming from the set S, i.e. if all si,j are S-units. In this paper, we show that no S-Diophantine quadruple (i.e. m=4) exists if S={3,q}. Furthermore we show that for all pairs of primes (p,q) with p <q and p ≡ 3 mod 4 no {p,q}-Diophantine quadruples exist, provided that (p,q) is not a Wieferich prime pair.