In addressing this claim, let us first note the full statement of James,
"Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man:" (James 1:13)
The single Greek word which is translated "cannot be tempted" is apeirastos, a negative construction derived from peirazo, which is a word meaning "to endeavour, scrutinise, entice, or discipline". The statement on James' part is a statement of nature or charactre. He is saying that God's essence and innate charactre is such that evil is not a temptation for Him, that He does not need discipline or difficult endeavour to keep from sinning, and the obvious contrast in the passage is that of man, who is easily tempted after his own lusts and enticed by temptations directed at his own weaknesses. It should be noted that James 1:13 is not necessarily saying that there will not be those who, at various and sundry times, may *try* to tempt God.
In its comment on James 1:13-15, the Wycliff Bible Commentary notes that James was probably responding to a doctrine which had developed in Judaism during the intertestamental period known as yetzer ha ra', "the evil impulse". This doctrine stated that since God had created everything, He had also created the impulse within man to do evil. As such, this would ultimately make God responsible for man's sin, since the impulses tempting man to sin were created by God and ultimately fall back onto Him for responsibility. James is clearly opposing this doctrine through his statement that God cannot be tempted by evil, and that He does not tempt man. This is a responsibility statement which falls back onto the innate charactre of the subjects under discussion - God and man. It places responsibility for man's sin squarely on man himself, since God's charactre is such that He neither created nor motivates wickedness on the part of man.
The examples given as suggesting contradictions with James 1:13 neglect to take into account the deeper meanings and cultural context behind James' statements. The verse is not saying that someone may not at some point attempt to tempt or test God. More, it is saying that they will not succeed in their effort. The children of Israel could not truthfully call God's provision for them into disrepute in Exodus 17:7, and Satan could and did not succeed in inducing the Lord Jesus to commit evil by succumbing to his temptations in the Gospel accounts. As such, God in all points in Scripture is shown to indeed be apeirastos, impossible to induce into falling to temptation to sin.