  We investigate Ramanujan congruences for the function which counts the
overpartitions of n with restricted odd differences. In particular, we show
that only one such congruence exists. Our method involves using the theory of
modular forms to prove a more general theorem which bounds the number of primes
possible for Ramanujan congruences in certain eta-quotients. This generalizes
work done by Jonah Sinick. We also provide two congruences modulo 5 for this
function.
