I am not sure what you mean when you say "local events". If it is not a registered or authorized AKC or similar Club event, then I would think you should be able to rent table space - just like anyone else. If it is some sort of official dog show with governing bylaws and restrictions, then you simply will not be allowed to participate (if that is their decision). You might want to try and get a permit from the associated community or bldg manager and set up your own display outside of the official event. Like vendors outside of a concert, game, etc..