quaternionic automorphic representations are one attempt to generalize to other groups the special place holomorphic modular forms have among automorphic representations of $gl_2$. like holomorphic modular forms, they are defined by having their real component be one of a particularly nice class (in this case, called quaternionic discrete series). we count quaternionic automorphic representations on the exceptional group $g_2$ by developing a $g_2$ version of the classical eichler-selberg trace formula for holomorphic modular forms. there are two main technical difficulties. first, quaternionic discrete series come in l-packets with non-quaternionic members and standard invariant trace formula techniques cannot easily distinguish between discrete series with real component in the same l-packet. using the more modern stable trace formula resolves this issue. second, quaternionic discrete series do not satisfy a technical condition of being ``regular", so the trace formula can a priori pick up unwanted contributions from automorphic representations with non-tempered components at infinity. applying some computations of mundy, this miraculously does not happen for our specific case of quaternionic representations on $g_2$. finally, we are only studying level-1 forms, so we can apply some tricks of chenevier and taïbi to reduce the problem to counting representations on the compact form of $g_2$ and certain pairs of modular forms. this avoids involved computations on the geometric side of the trace formula.