I would avoid real jousting. There are some clubs in the US that do the real thing, and there is a TV show on it as well. Some of those people get really badly hurt. I've watched 2 episodes of the TV show and in the second episode one of the men got taken away in an ambulance with a head injury.
I watched one event by the local jousting club. Getting knocked off sure looks like it hurts. Even at the trot on a pony (which was all they were doing).
My friend was part of a jousting club in her youth. I don't remember the entire story but one of the men in the club almost got killed. Ended up getting knocked underneath the horse with the horse dragging him.
As far as hitting targets... As a kid I tied a board to a tree so it would swing. I would take a broom handle and hit it. I also put swimming pool rings in the fence (large O rings). I would ride by and try to catch them on a stick.
Another game I liked is where you put a pot of dirt on a fence post, and try to put the flag in the pot with the fastest time without knocking the pot off the fence.
Easter egg hunts on horse back are fun!