Richard Swinburne’s case for God can be broken down into five phases:

I.  The Coherence of Theism
II.  The Nature of the Universe as Evidence for God
III. The Nature of Human Life as Evidence for God
IV.  Religious Experience as Evidence for God
V.  The Life of Jesus as Evidence for God

Phase I is presented in Swinburne’s book The Coherence of Theism (revised edition, hereafter: COT).  He argues that the assertion ‘God exists’ makes a coherent and contingent factual claim.  If he is correct, then the question ‘Does God exist?’ cannot be answered by logic and conceptual analysis alone; one must make use of empirical evidence in order to rationally determine an answer to this question. 

According to Swinburne, the assertion ‘God exists’ does not make a logically self-contradictory claim (so this claim is not a logically necessary falsehood), nor is it a logically necessary claim (it is not a logically necessary truth that ‘God exists’).  It is logically possible that ‘God exists’ is true, and also logically possible that ‘God exists’ is false.

Swinburne believes he has shown that the concept of ‘a contingent God’ is coherent. That is to say, if we conceive of God with the various traditional attributes other than ‘necessary being’, then Swinburne thinks he has provided good reason to believe that the assertion that ‘God exists’ makes a coherent statement:

The argument in Part II [Chapters 7-12] has been that it is coherent to suppose that there exists eternally an omnipresent spirit, perfectly free, the creator of the universe, omnipotent, omniscient, perfectly good, and a source of moral obligation—so long as ‘omnipotent’ and ‘omniscient’ are understood in somewhat restricted senses.
(COT, p.241)

Swinburne constricts the concept of being ‘omnipotent’ a bit, but does more serious alteration to the concept of being ‘omniscient’. Roughly speaking, God has a difficult time knowing the future, because God is perfectly free, which means that what has happened in the past does not determine what choices God will make in the present. Since God is in control of everything (because of his omnipotence and omniscience), everything that happens involves God choosing to make it happen or at least to allow it to happen, so since God cannot predict his own future choices, God’s knowledge of future events is very limited. 

To the extent that human beings have free will, God is also not able to predict the choices humans will make.  God knows every fact there is to know about what exists now and what has occurred in the past, but that is not sufficient to infer the choices that will be made by perfectly free persons now, or by partially free persons (like humans), because the events of the past do not determine any choices made by perfectly free persons now, nor do they fully determine all choices made by partially free persons.

Swinburne, however, also thinks that traditional theism holds the view that God is a ‘necessary being’, and that it is not possible to give a direct proof that the assertion ‘God exists’ makes a coherent statement, if interpreted this way. On the other hand, if it is possible to give inductive evidence that confirms the existence of such a God, that, according to Swinburne, will give us good reason to believe that the assertion ‘God exists’, where ‘God’ is conceived of as a necessary being, makes a coherent claim:

If this claim of Part III [i.e. that God, conceived of as a necessary being, exists] is to be a coherent claim, the words in which it is expressed have to be taken in an analogous sense.  Given that the words are so taken, I was unable to prove in any direct way either that this claim was coherent or that it was incoherent.  However, I pointed out that there could be an indirect proof of coherence in so far as there was inductive evidence for the truth of what was claimed.
(COT, p.241)

More specifically, Swinburne modifies the meaning of the word ‘person’, stretching the meaning of this word in order to avoid the problem that in the case of ordinary persons, it is always coherent to suppose that a person can lose or gain power or knowledge while remaining the same person.  If God is to be conceived of as a necessary being, then, according to Swinburne, God must be an odd sort of person such that he cannot be coherently conceived of as losing power or knowledge (see COT, Chapter 14, especially p. 283-284).

Because Swinburne alters the meaning of the word ‘person’ and related concepts, he cannot directly prove that the assertion ‘God exists’ makes a coherent statement:

I cannot now myself prove either that the quoted statement [to the effect that God is a necessary being] is coherent or that it is incoherent.  The stretch of meaning of the words involved has left me without arguments of the normal kind for or against coherence. 
(COT, p.288)

In Chapter 3 of COT, Swinburne clarifies what he means by a ‘coherent statement’ (p.30-38), as well as how one goes about showing that some particular assertion makes a coherent statement (p.38-50).  After describing how to give direct arguments for an assertion making a coherent statement, he also describes how one can give an indirect argument for this:

So although I do not rule out the possibility of useful inductive arguments of other kinds to the coherence of statements, the only kind of inductive argument for which I see much future is one of the above kind from known factual premises p, to a non-analytic claim q, evidence for q‘s truth being evidence that q is coherent.  Such an argument I shall call an indirect argument for the coherence of q …
(COT, p.49)