In The Enchiridion, for example, there is only the most token mention of Gods, piety and divination. Only 3 chapters of 53 make any noteworthy reference to these things. They amount to advising that we accept fate rather than fight it, and don't look for guidance from the Gods in matters where our reason will suffice. That's about it. The rest of the text is about molding our perceptions, opinions and habits, using logic to live the good life, and seeking virtue for its own reward, rather than any idea that we could gain rewards in the afterlife or avoid damnation through worship. You could easily substitute "fate" for "Gods", and in most cases the text would make just as much sense if not more. In fact, fate already is featured much more prominently than God.
The stoics could not have made a finding of no God or even doubted God and continued their work, as they would have faced exile or execution, and nobody would have dared to accept their teachings in that case for fear of suffering the same fate. They simply were not allowed to not believe. In that context, what you see in the text can be taken as consistent with their doubting or not believing, yet holding back from explicitly saying so. You can say from the text that they went as as far as they were able to tell people to think for themselves. And, they had texts for the public, texts for advancing stoics, and texts withheld from all but the inner circle, which may have had a different take on the issue. Maybe @LuckyR can weigh in, as he made me aware of this.
I consider myself agnostic, and I take stoicism rather seriously, and don't feel that my lack of belief is inconsistent with the philosophy. It's entirely possible that if Epictetus or Seneca or Zeno could weigh in today, when they could speak freely, they might be OK with agnostics or atheists joining up, and might even be counted among them.
Below are the only references I see in the Enchiridion to religion, and I think they are consistent with what I said above. Recall that there are 50 other chapters which focus on virtue, perceptions, duties, logic and emotions. It's 10 to 1 or more logic and psychology over religion.
31. Be assured that the essential property of piety towards the gods is to form right opinions concerning them, as existing "I and as governing the universe with goodness and justice. And fix yourself in this resolution, to obey them, and yield to them, and willingly follow them in all events, as produced by the most perfect understanding. For thus you will never find fault with the gods, nor accuse them as neglecting you. And it is not possible for this to be effected any other way than by withdrawing yourself from things not in our own control, and placing good or evil in those only which are. For if you suppose any of the things not in our own control to be either good or evil, when you are disappointed of what you wish, or incur what you would avoid, you must necessarily find fault with and blame the authors. For every animal is naturally formed to fly and abhor things that appear hurtful, and the causes of them; and to pursue and admire those which appear beneficial, and the causes of them. It is impractical, then, that one who supposes himself to be hurt should be happy about the person who, he thinks, hurts him, just as it is impossible to be happy about the hurt itself. Hence, also, a father is reviled by a son, when he does not impart to him the things which he takes to be good; and the supposing empire to be a good made Polynices and Eteocles mutually enemies. On this account the husbandman, the sailor, the merchant, on this account those who lose wives and children, revile the gods. For where interest is, there too is piety placed. So that, whoever is careful to regulate his desires and aversions as he ought, is, by the very same means, careful of piety likewise. But it is also incumbent on everyone to offer libations and sacrifices and first fruits, conformably to the customs of his country, with purity, and not in a slovenly manner, nor negligently, nor sparingly, nor beyond his ability.
32. When you have recourse to divination, remember that you know not what the event will be, and you come to learn it of the diviner; but of what nature it is you know before you come, at least if you are a philosopher. For if it is among the things not in our own control, it can by no means be either good or evil. Don't, therefore, bring either desire or aversion with you to the diviner (else you will approach him trembling), but first acquire a distinct knowledge that every event is indifferent and nothing to you., of whatever sort it may be, for it will be in your power to make a right use of it, and this no one can hinder; then come with confidence to the gods, as your counselors, and afterwards, when any counsel is given you, remember what counselors you have assumed, and whose advice you will neglect if you disobey. Come to divination, as Socrates prescribed, in cases of which the whole consideration relates to the event, and in which no opportunities are afforded by reason, or any other art, to discover the thing proposed to be learned. When, therefore, it is our duty to share the danger of a friend or of our country, we ought not to consult the oracle whether we will share it with them or not. For, though the diviner should forewarn you that the victims are unfavorable, this means no more than that either death or mutilation or exile is portended. But we have reason within us, and it directs, even with these hazards, to the greater diviner, the Pythian god, who cast out of the temple the person who gave no assistance to his friend while another was murdering him.
52. Upon all occasions we ought to have these maxims ready at hand:
"Conduct me, Jove, and you, 0 Destiny,
Wherever your decrees have fixed my station."
Cleanthes
"I follow cheerfully; and, did I not,
Wicked and wretched, I must follow still
Whoever yields properly to Fate, is deemed
Wise among men, and knows the laws of heaven."
Euripides, Frag. 965
And this third:
"0 Crito, if it thus pleases the gods, thus let it be. Anytus and Melitus may kill me indeed, but hurt me they cannot."
Plato's Crito and Apology