That is what we tried last time, completely casual competition with relative open themes. End of the month anyone got to pick their favourite photos. Everyone always says they are interested in such things but after a few months there were no entries.
You can try and restart it and see what happens. Doesn't take much to organize and then just make a post. Some broad topics for starters: Land & city scapes, nature, people, texture, B&W, perspective, big & small, emotion, balance, symmetry, circle....
IMO, you either need to give people 2-3 months, or let people add entries from their back-catalog, e.g. if the topic is nature I might want to add a photo form 2 years a go because within a single calendar month I might not get out with my camera at all. The easier it is to contribute the more people might take part.