Yes. There are 2 county beach parks which offer overnight tent camping. Papohaku Beach Park on the west end and One Ali’i Beach Park on the south side both have rest rooms and shower facilities. You’ll need to acquire camping permits from the parks and recreation department which run $3.00 per night. It’s a good idea to call in advance. 808.553.3204
There is also Pala’au State Park in Kalae for tent camping. It has restrooms, but no showers. Check the camping page for all the Molokai camping details.