List of Logical Fallacies Found With This Line of Reasoning:
Appeal to Consequences:
"If God doesn't exist, there would be no basis for morality and that would be bad, therefore God exists"
(Just because you want something to be true doesn't mean it is)
Bare Assertion Fallacy:
"Without God, there would be no morality/logic/etc."
(You find these unsupported assertions all over the place in even classic apologetic arguments)
Straw Man Fallacy:
"Atheists believe there is no God so how do they account for..."
(Skepticism is not a belief system but an approach to other belief systems, asking other beliefs to meet their burden of proof)
Shifting the Burden of Proof:
(continued from above) "...so how do they account for morality/logic/universe/etc. without God?"
(Saying "I don't know" does not require that the person admitting lack of knowledge explain anything.)
Argument from Incredulity:
"I can't imagine how we could have morality/logic without God."
(Your inability to comprehend something does not mean it's not true)
Argument from Ignorance:
"GodDidIt. GodWillsIt. GodIsIt. GodDoesIt. GodVerbIt."
(Just because we don't know doesn't mean made up answers are true)
Non-Sequitur:
"You don't know everything, therefore Jesus."
(Conclusions must actually follow from the proofs offered).
Special Pleading:
"By 'God', I of course mean Jesus. This argument doesn't prove anyone else's god. It can't be used for Zeus, Odin, Ra, Allah, et. al."
(It's hypocritical to ask for a lower standard of proof for your favorite beliefs than one you'd demand for someone else's beliefs.)
Begging the Question:
"We know that Yahweh is good because we define Yahweh as the source of goodness. And since Yahweh is the source of goodness, we know that Yahweh is good."
(We often see contrived definitions like this to escape Euthephro's Dilemma ("Is something good because GodWillsit or does GodWillIt because it is good? If the former, then divine command morality is just might-makes-right and, if the latter, morality exists outside of God and therefore God is not required"). The apologist will seek a third way and say that Yahweh is the source of goodness. Beyond the problems that this is a contrived definition established by bare assertion in order to work backward toward a desired conclusion, such thinking quickly devolves into circular reasoning about the goodness of Yahweh and how we can know that he is good.)
Ad Hominem Tu Quoque:
"Look, you have your faith in the basal assumptions of science. I have my faith in Jesus. It's a wash." -or-
"Everyone has presuppositions."
(Instead of defending against accusations, the other person offers a "you do it too" defense, whether or not it's true. As with the Ad Hominem, it's OK to question the character of the other person as long as it's not a substitute for an argument).
False Equivalency:
See above.
(the axiom that repeatable experiments will tell us what we can predict in the future or that reality is real and not just a computer simulation, etc. are not the equivalent of a faith in an Iron Age holy book that makes all manner of supernatural assertions contrary to how the observable universe operates).
Confirmation Bias:
"The Bible said (some vaguely worded prophecy) and look, this happened."
(Don't start with a belief and look for evidence to confirm it).
Ad Hoc Hypothesis: (my favorite)
"Well, maybe... well, maybe... well, maybe..." (repeat endlessly until all contrary evidence is dismissed)
(If you have to keep inventing reasons, often improvised and pulled out of the air, why contrary evidence doesn't count or invent unlikely, obtuse interpretations of scripture to fit what you want to believe, eventually the opponent can invoke Occam's Razor and go with the simplest explanation that scripture really does say what it appears to say).
Misunderstanding of Logical Fallacies:
"Explain why science works better than faith. Don't say 'because it works' or I'll call that circular reasoning."
(Presuppers don't understand what circular reasoning is. If you write a book and footnote another book, that's not circular reasoning (using books to prove books) because you have different authors. If different people get the same results doing the same thing, it's not circular to say it works because the corroborating results come from different sources.)
Misunderstanding of Skepticism:
"You have a bias against miracles."
(Skepticism is not an agenda but a rational approach to extraordinary claims, one that the religious believer applies to other people's religions. A lack of a belief is not a belief. The assertion of miracles is an extraordinary claim that requires a proportional amount of evidence, more evidence than is required for mundane claims like "I had a hamburger for lunch today". These are the rules that we operate by in every area of our lives outside our favorite beliefs. See also Special Pleading.)
Please feel free to add any I missed.