The town of Puerto Obaldía in Panama has a Colombian consulate Colombian consulate (not an honorary consulate). There are some photos of the consulate here.
Puerto Obaldía only host 672 people according to Wikiaccording to Wiki.
This town is literally in the middle of nowhere. It has no access to any roads (its located in the Darien gap) and only has a small airfield to connect it to the outside world.
I believe it could the smallest non-capital city with a full time operational consulate in the world.
https://en.m.wikipedia.org/wiki/Puerto_Obald%C3%ADa