  For full shifts on finite alphabets, Coelho and Quas showed that the map that
sends a H\"older continuous potential $\phi$ to its equilibrium state
$\mu_\phi$ is $\overline{d}$-continuous. We extend this result to the setting
of full shifts on countable (infinite) alphabets. As part of the proof, we show
that the map that sends a strongly positive recurrent potential to its
normalization is continuous for potentials on mixing countable state Markov
shifts.
