Let me begin by saying that 'theistic' does not imply the existence of a single deity only, that would be 'monotheistic'.
This brings me to the point that the best answer to your question depends on the God you're trying to explain.
Are you looking for a term which encompasses all deities, or a particular deity; are you trying to include non-personified deities, or non-deific spiritual constructions too?
If you want to be inclusive, I'd opt for words like spiritual, which is nicely open-ended; Godly, which is a little awkward because of its use as an adjective for piety or devotion; or Divine.
"A series of deific visits" is good middle-ground... It doesn't specify a deity, but to go into any more detail would require tacking on ugly words like Judeo-Christean or Abrahamic before your adjective. I suppose you could take the slightly more specific wording, and call them "monotheistic visits", but that is awkward and only serves to draw attention to the fact that you're lacking a word to describe the particular deity.
If we were being poetical, rather than scientific with our naming, we could allude to a deity through that deities characteristics ie: 'a series of omniscient visits', but that implies that omniscience is part of the visits themselves (demonstrated through the occurrence of these visits, etc). This could perhaps work better with a word like transcendence; if the visits were perceived to have occurred outside of the realms of space and time. This also works for terms like celestial.
A third option (and probably the best) is to avoid the question entirely and simply specify your deity by re-ordering your sentence as "in a series of visits from ____".