Theta-type congruences for colored partitions

We investigate congruence relations of the form $p_r(\mathrm{\ell }mn+t)\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{\ell })$ for all $n$, where $p_r(n)$ is the number of $r$-colored partitions of $n$ and $m,\mathrm{\ell }$ are distinct primes.