I don't agree that you should automatically whip your kid off a ride that they were on first simply because someone with money shows up. In my case I give my kids a heads-up that someone else is waiting for a turn (if it is one of those single kid ride numbers) or if it is a multi-kid one I tend to do a quick head count and if there are enough spaces then I dont expect to ask my child to get off. TBH though we are rarely on those things long enough to really have any fuss.

If i have a coin i will throw it in and if there are kids looking like they want to get on, i always ask if they want to join in too...the more the merrier!