Tournament Joust is a free print and play game with some really good looking jousting mechanics. It has paper knights, but you’ll want to swap in your own miniatures.
Jousting Tourney Rules
Al Hewitt and Ric Willey offer Jousting, a set of free wargames rules for medieval tournaments.
To Cry A Joust
To Cry A Joust is a set of free wargames rules for jousting combats.