There's exactly one divine Warlock PrC (Eldritch Disciple), and that advances invocations and divine spells separately.
Sure you can take up "+1 level of existing spellcasting class" PrCs. Even if they have some divine flavor, those classes aren't what I consider divine spellcasting classes.
You can't take up "+1 level of existing divine spellcasting class" PrCs (to progress invocations, that is), only "+1 level of existing arcane spellcasting class" ones. That's what I mean: Warlock SLAs are considered arcane, as far as I can see.