'A Tragedy of Telepaths' starts with Lochley giving her log entry as June 16, 2262, but yeah, aside from season finales and premiers (which always take place around new years) specific dates are few and far between. When they are mentioned it's usually retrospective, like "remember back in August when...." Which is fine, because who the hell remembers uses dates in conversation anyway?
One assumes they were intentionally avoided for the most part because it allowed JMS some wiggle room in terms of continuity. Trying to track the specific days and times of fictional events can be a nightmare and a writer can really paint themselves into a corner over time unless they're *very* meticulous. Even a show like '24' which supposedly took place in real time could never get it 100% consistently to the minute.