PSMSL monthly sea-level data
The PSMSL dataset contains 1214 series of monthly mean sea-level data, from 1 to 183 years long.

I am not sure what the reference is for individual stations: the geoid or (moving) land. Please consult their web pages.

The dataset is updates once a month from PSMSL. However, PSMSL depends on the data being sent to them, so the series do not quite extend to the last month in general.