I'm president of a new club we would like to invite people but we can't figure out how to do that...

The invitation list only comprises those people in your boat list, either neighbors that Wooga gave you or your FB friends. If you want those particular people to join your new club, have them search the club name and apply to your club. Make sure you know their island name, so you can recognize them when they appear in your club inbox. Alternatively, you can find the individual on FB if you know their FB name, send them friend requests, and once they accept they should then appear on your boat list and you can invite. If they are already FB friends and are not appearing in your boat list, you will have to log the game out of FB and reconnect.