Atheists, what are the most convincing theist arguments you heard of?

[RoadRunner79]

---

I can say that the first mover had no cause (never began to exist). This argument doesn't assume god at all and doesn't beg the question. Part of the KCA is to deduce characteristics by logical analysis of the properties of this cause, so the argument demonstrates this first cause is uncaused, personal creator, beginningless (eternal), timeless, spaceless, changeless (immutable), immaterial, and powerful. 
This is true and is a working objection, matter and energy would have began to exist in the beginning of the universe, so to say that whatever comes into existence requires some external cause of some kind is to say a lot. We don't even know if the universe began to exist, which is why I sometimes hesitate to talk about the big bang as the beginning of all existence. 
Its basis is faulty, but I wouldn't say that concluding design from observation is inherently ignorant as opposed to random natural processes. It is just another explanation. It may be simpler to state that life is designed as opposed to explaining random natural processes, but accepting an explanation over another simply because it is more complicated to explain would be a fallacy. Also, design need not be from God, in fact, that may be a farfechted conclusion even if we are to suppose that certain features of the universe are designed.
You mean the argument from miracles?

---

Are you saying that the identity (as a deist or religious person) of the person impacts the strength of their arguments or that the deist god (as different as it may be from all the other religions) is more supported by what we know than the religious gods?

---

I'm only dealing with your first paragraph here. The main problem with the uncaused causer and all allied arguments is that they all posit a being which violates a rule they say is universal. The uncaused causer goes, all things are created>therefore they must have a creator>go far back enough and you will find a thing that has no creator>god exists QED.

As you can see, clause three violates clause one, either god had a creator (which leads to the turtle problem) or it is not necessary for everything to have a creator (thus negating the chain as proof for god). Every argument along that strain in the monotheistic theologies has that fatal flaw.

Do you have problems with Newtons first law of motion as well?
The argument in a better form, states that everything that begins to exist, has a cause.   It is not violating a rule as you infer. (note: I didn't go back in the thread, so I'm not commenting on anything specific to the conversation or what may have been presented to you.)

 I actually find it interesting, that even when presented with this argument, that there are a good many, who seem to remove or not hear the "begins to exist" part in there attempted refutation.  Much like the specification of an object in motion in Newton's theory, there is an important reason why "begins to exist" is in this formulation. 

And you are correct, that the argument does not say that everything requires a cause; only that which begins to exist.  And this alone doesn't point to God.  There are other parts of the argument however, which infer from the available evidence the what qualities would be sufficient of that cause.