It's set on Titan, where there is a small colony from Earth, and there is no possibility of an ordained minister arriving within the next couple of years.
Searches I've tried:
duties of lay preachers
lay preacher performs wedding
lay preacher performs funeral
What I mostly seem to find is things saying that a lay preacher can't do these things, but given the special circumstances I wondered whether any of the mainstream Christian churches would make some sort of special dispensation.
Thanks to everyone who commented - I've decided to go with Baptist in the end, it's one that everyone has heard of and it's a common enough sect that there would probably be several in the colony.