Character bounces on descending platform.

Hey all. I'm trying out something for a game idea I have which would put the player on a ship being attacked by a sea monster. It's from a side/mario-style perspective. One of the first problems I've run into is that when the ship rises and falls a bit to simulate being on the sea, the player falls a bit, hits the ship, falls a bit, hits the ship, etc, making a little bouncing motion. I suppose increasing gravity could help, but I'm hoping there is a workaround, as I'm hoping to be able to have the ship launch the player at times. (One side of the ship suddenly blasts upwards, launching the player if they're near it.)

Does anyone know what I could do to make this look cleaner?