This is a very easy one for an infallibilist to deal with. There are conflicting accounts of (Old Testament) Saul's death in battle. First 1 Samuel 31:4:
There's a similar account at 1 Chronicles 10:4. However, this is 2 Samuel 1:8-10:
(Incidentally, one of the infidels.org lists of contradictions quotes the wrong verse; the verse in which it is the Amalekite who is killed.)
Now, the most simple and obvious explanation for the contradiction is that the Amalekite is lying about it. He may have thought that by claiming to have killed Saul out of mercy, he would be rewarded.
One more thing: another list of contradictions claims that these verses contradict 1 Chronicles 10:14, where it's stated that God killed Saul. However, it's fairly obvious that this means that Saul dying in the battle was God's will.
As you probably know, I'm not an infallibilist. Although the explanation I give above is a possible one, this does not necessarily mean I favour it. It is entirely possible that the two accounts of Saul's death (suicide vs. mercy killing) originated in the chaos of battle.