Have them all live in the same house, perhaps? So they can all share the same PC with a copy of vMix :)

Being more serious, I'm unaware of a way of preparing a Playlist outside of vMix so that it can be simply imported when needed. To quote from the Documentation, "Opening/Saving a PlayList
PlayLists are linked to the currently active Preset in vMix. This means any saved playlists can only be loaded alongside the preset in which they were created."

Obviously each member of the team can create content at home (eg images, graphics, video) that can be used as an element in a Playlist, but I think you would have to appoint someone to be the "Playlist compiler" (with vMix on their PC) to whom the other members would send their content (e.g via WeTransfer, shared GoogleDrive folder, etc) together with a script/running-order of how the Playlist should be compiled.

No there isn't. You probably had the best solution with a laptop which the appropriate member could take home when it was their turn to create the next Playlist.

We're a church so computer, cameras, sound system etc. etc. are not turned on when no one is in the building.

We get most of the stuff (scripture, liturgy, songs, bumpers) during the week with some stuff coming in Friday night or Saturday morning. The team members have full time jobs (not in the church) and usually plug away at vMix on Friday or Saturday evenings. We also live quite north of the equator and, in a few months, no one is going to be happy driving to church in the dark in subzero temperatures. They'll probably be the only person in a freezing building as heating is usually turned way low during the evening to conserve energy.