The ASDS (drone ships) use diesel[1] for stationkeeping but they use tugs[2] to get from the port to the landing site & back.

I can't get engine details on the tugs[3], but wikipedia says[4] tugs often have locomotive diesel engines.

1 - https://www.thrustmaster.net/out-drive-propulsion-unit/porta...

2 - https://www.reddit.com/r/spacex/wiki/asds#wiki_ships

3 - https://www.marinetraffic.com/en/ais/details/ships/shipid:43...

4 - https://en.wikipedia.org/wiki/Tugboat#Tugboat_propulsion