You could start by adding `sports=*` to a conference/exhibition/event center object if it is mainly for the latter.
>But these facilities are not specifically any of these but all of these.
Sports venue tags could possibly co-exist with event venue tags. I would suggest `leisure=sports_hall`, which is already often used as a venue for other events in schools and communities. `=sports_centre` usually implies a permanent one, available for training mostly, only holding sports events sometimes. `=stadium` sounds too big for these.
Conversely, I could imagine someone tagging a smaller, local sports hall with `amenity=events_venue` (alternatively `leisure=events` if they regularly hold non-sports activity. (if it's not a `=community_centre` already)
>I would say they are closest to a convention center (that doesn't seems like an existing tag)
It is cited as American English of "conference centre".
>Maybe an events center? But that is just a proposal.
Both `amenity=conference_centre` and `amenity=exhibition_centre` are "proposals". I would support event center for reasons written there.