It helps to have all four extra activities (Butt Battle, Waterslide, etc.). 
Go to a vacated area where it is just the two of you. Play a mini-game and let 
your partner win. Another contributing factor is winning volleyball games. If you 
lose, your Relationship points will decrease. Note: The Waterslide activity will 
not increase your Relationship points, because it is a solo mini-game.