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Small note: I have aimed these rules are promoting two virtues. The first virtue of is that we ought to create an environment that encourages theists to stick around so long as they are posting quality stuff. This involves a fundamental attitude change in how users use the sub. This does mean that we are going to lose some posters, but I promise you they are not the posters you are going to miss. The second virtue is we should have a community that doesn't think it is appropriate to respond to a long OP with a sentence long "GOTCHA" answer.
These are going to take some moderation but the best subreddits on reddit have a fair amount of moderation. I have stolen, and mostly weakened, rules from subreddits like r/ChangeMyView, r/AskPhilosophy, r/AskHistorians, /DebateReligion. There is no reason that we can't be closer to these subreddits in regard to the quality of the posts.

Articulating these rules to the subreddit will also lessen the amount of work we have to do as a modcrew: if users understand the rules and respect the effort mods make to change the subreddit, then they will report stuff that violates the rules. Getting this flagged up means we don't have to trawl through each and every post. Look at u/Taqwacore as an example of how quick it is to moderate if you trust your reports.
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1. The easiest thing to do is to change the sidebar. As it exists right now it has way too much text and the links to popular arguments aren't particularly well framed for people who just aren't at all educated in the topic. I suggest that we do something closer to r/DebateReligion's sidebar. It is brief where each rule is understood in less than 5 words. If you hover over the rule you get more expansion.
This involves, too, removing that definition of "atheism". I recommend giving a broad definition of atheist, about a sentence long, in the sidebar and say "if you disagree with this provide your own definition in your OP." This does two things: it has a call to action that promotes engagement by asking for a definition and it tidies up the bar. Having these calls to actions littered around is easy enough to do and something that should help with getting the sort of response we want.

After talking with other mods, some thing that this would lead to endless fighting over what “atheist” means. What I suggest is that if we do keep a long definition in the sidebar that we moderate around blatant ignorance concerning that definition.

2. We should remove the Thunderdome. I think that the Thunderdome promotes the worst attitudes of the community; we shouldn't allow a space where users are now allowed to post low effort garbage because the theist isn't engaging. If the OP doesn't engage, I have no problem removing the post.
A middleground has been proposed: if the OP is being rude for no reason instead of thunderdoming it we would lock the thread, message the OP and if we got a reasonable reply would unlock it. If the OP continued being a dick we ban OP.

3. And here is how we get theists to make sure they hang around: r/CMV asks that OPs be able to respond within an hour for a few hours after posting. Having this rule allows you to moderate out weaker posts based around low-effort questions. It is also easy enough to enforce.

4. You might be asking yourself now "what constitutes Low-Effort?" and I think that is a good question. That is a discussion we can have, but now I want you to imagine it as badly articulated, short and bad-faith posts. Intuit it for now and we can hammer it out specifically later.

5. Fix flairs so they aren't ugly.

6. A recommendation that r/DebateReligion has is that people frame their topic as a Thesis; that is a short and clear statement of the position that they are going to be defending. This also doubles as a good time to say that we can edit things in before people post; at the post page you can have information that functions as a call to action.
I should say that recommendations don’t have to be enforced. Instead I want it somewhere visible so that people might read it.

7. We should try to encourage high quality responses if we are going to ask a fair amount from our posters; we should encourage posters to quote the text from the OP that they have a problem with. We should also encourage them to *defend* their objections. As an example, a bad response is "but I am a Materialist." A good, or at least better, answer is to say "This premise doesn't work with Materialism. Here is why I think that, and here is why I think we ought to be a Materialist." We don't have to police the quality of the arguments, but we should police their form. If you have a proper structure, and this is what you hammer into first years in uni, the rest should follow. AT minimum, it frames the arguments clearly and makes it easier for the OP to respond. When I wrote this out I understood it as more negative; not so much that we should aim at uni quality but we should do a better job at removing rambling.
This isn’t meant to imply that posts should be at a uni quality. They are, for one, a lot shorter. But I do think that we should have an checklist on the page before posting a thread that says “have you given an argument and defended it?” And so on. We can’t remove posts that aren’t great, but we can remove posts that don’t adhere the very basics of a debate.

8. Something that I haven’t given much thought, but I’d like to hear your opinions on is how we deal with clarification questions. I think we need a space for these, and we shouldn’t police them like they are arguments. Maybe ask users to say “just a clarification here:” or something. The same goes for suggestions or so on.

9. Similar to the thesis idea but thought of later: we should be reminding people do define all the terms they use. So much time on this sub is wasted by people talking past each other.

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Now we are on to some things that I think would be useful in promoting the rebirth of the subreddit.
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1. I think that the arguments on the sidebar are worth going over, but I think we should go through them in threads. A short write up, that I am happy to do, on one of these arguments could happen once a week. I think they should have the form: here is the argument, here are some common objections, and here is how more recent literature deals with these. By bringing in info beyond the Wikipedia page we stop these being so stagnant. We should also include a call to action here: ask users which premise they find to be the weakest, or which objection seems the most promising. We can sticky these over the course of the week to allow users to argue about it. Once they are done, we can link them in the future weekly threads. This lets the users engage in a meaningful way & as well as gives us a bank of the popular arguments to refer to users who end up posting the same old Cosmological Argument.

2. I think having monthly rewards for good posts seems a good idea. Have a thread asking users to post their favourite argument from the subreddit in the last 30 days and then upvote the ones they like. The best, or most popular, can get gilded. I am happy to pay for that once a month. They should also get a flair that says “best argument of July 2019” or something like that. I have noticed there is a flair in the subreddit for doing something like this, but I haven’t seem it used. I think, again, calls to action like this keep people motivated and who doesn’t love recognition for good work?

3. In the old days a few of us who ran the IRC for this chat as well as for r/DebateReligion used to post rabble threads. These were weekly threads posted in religious subreddits, with the permission of their moderators, inviting people to either the subreddit or the chat. If we work to develop an attitude of openness that tries its hardest to promote good work, then people are going to linger. Plus having these threads ensures a constant trickle in of theists which is something that we need.