So the news that First Church Atheist has already fractured only means it needs the equivalent of a papal office, and that a TEC bishop would probably do just fine. But if a Vicar of Nothinginess is too much to stomach, then may I suggest the various atheist denominations follow a Protestant paradigm.
First, compose a confession of faith that sets out your distinctives. Perhaps your atheist church doesn’t believe in God but believes in aliens who may have created Earth, or life on Earth, as some grand experiment, or perhaps as a way station (see Kurt Vonnegut’s Sirens of Titan).
Or maybe you are 99% certain that there is no god, but are willing to admit that a 1% possibility qualifies as agnosticism, and so agnostics are welcome so long as they refrain from speculating on attributes of that hypothetical deity.
Or maybe you are 110% certain there is no god and equally convinced that anyone believing in such a notion is a threat to the future of humanity, even though the overwhelming majority of humanity believes in the supernatural. So you may want to insist that any member of your church shun friends or family members who are theists.
Some of you will not want to use the word atheist per se, for fear it will scare aware “seekers.” You may want to follow the Unitarian Universalist model in that case. You also may not want to claim that only atheists are destined to eternal nothingness upon death. Emphasize that all people share that fate. Exclusivism breeds arrogance.
The list could go on and on. Also, you should probably state explicitly whether you believe members of other atheist churches are also true atheists, even if in error about some incidentals, or are beyond the pale, perhaps closet deists. Pulpit and guillotine fellowship must be denied to them, of course.
Atheist clergy should be licensed. An atheist seminary, one associated with your particular denomination, is desirable. In short, any public college will do.
You may also want to construct a liturgy of some kind, or at least an order of blasphemy, to create a tradition that may “stick” with the younger generation. May I suggest one element—Ernest Hemingway’s immortal prayer:
Our nada who art in nada, nada be thy name thy kingdom nada thy will be nada in nada as it is in nada. Give us this nada our daily nada and nada us our nada as we nada our nadas and nada us not into nada but deliver us from nada; pues nada. Hail nothing full of nothing, nothing is with thee.
As for the equivalent of a eucharistic meal, you can’t go wrong with pot luck or empty calories.
Oh, as for the offering—cash only. No checks.
You may also want to end your services with an anti-benediction of sorts, something like the prayer of St. Francis.