Personally, I've found it ineffective, (and well, tedious), to present arguments for atheism against theists, particularly Young Earth and literalists, in the traditional sense--Claim, reasons, and conclusion. Usually, the atheists' reasons cannot overcome the theists' faith in the counterargument. Rather I now often choose to place the theist on the horns of a dilemma. I don't now about you; but, I am amused at the logical contortions that some theists, particularly Biblical literalists, will perform to quell their cognitive dissonance. P.T. Barnum would be proud. The argument goes as follows:

Proposition 1.
God created the earth literally as the Bible says. Six days, life in its present form, etc. (Yes.)
Consequently, evolution is not real and untrue. (Yes)

Proposition 2.
The cataclysmic story of the Noah and the Flood is a factual account. (Yes.)

Reasoning...
In the story of the Flood, all the animals (2 by 2 for unclean, or 7 by 7 for clean) were saved. That means every species was on that ship (because their disbelief in evolution makes it so). The Bible gives clear measurements to the Ark's size. That ship could not hold that much biomass and still float.
OR
Secondly, let's consider the flora. If the entire earth is covered with water for 40 days, then every land plant would have died. Even aquatic plants would be annihilated. I over watered my ficus over a couple of weeks, and it's lifeless. At best, the phytoplankton might survive.

So they are left with a finite number of animal and plant species at the end of the flood. Then explain the diversity of life.
or the flood story is allegorical because evolution is untrue.

Suggestions/Comments welcome.