GreyLord
Legend
I might run it as tapping into a plane for power. In this case each domain is a specific source of power which people can tap into.
Even without gods, there might still be religious organisation. They could be philosopher priests who gain their power from somewhere. Some of these religions might even have gods but those in the higher orders know that these gods don't truly exist.
I also like just having them as a different kind of spellcaster. The source isn't divine but it is differentiated from the workings of wizardry.
It is NOT odd that such an individual would want to play in someplace similar (such as Medieval Europe or Renaissance Europe). Even beyond the wrappings of history perhaps someone wants to play in a world like Dark Sun but where Divine Power still exists, or where there is no such thing as Divinity, but the idea of such powers can exist, powered by the strength of belief and faith.
Tapping a plane for power is a good idea. Each plane is in equivalent with someone's alignment or how they act.
Another could be tapping into someone's faith in something. For example, maybe someone is devoted to the idea of The Power of life or health, or perhaps to the power of creation or Water.
Their faith in such concepts could be the power that grants them the spells and abilities.
Another could be that they have patrons, similar to that of Saints. These patrons are NOT deific in nature, but they are Saints or Patrons over certain things and as such faith in these can also grant clerical spells and powers.
Warn your players about this ahead of time, but don't tell them what the side effects are. Let them wonder and be afraid. The side effects you choose should be creepy, weird, and fitting to a S&S genre. But don't make them detrimental; aim for troublesome and inconvenient. Like, a servant of the "god" manifests and provides aid plus collateral damage. Or, maybe the cleric starts going slowly insane each time they use this ability. Divine Intervention's actually a really cool ability, and you don't want this to be a nerf, more of a flavor thing.