This question has been burning in my mind for days now, and I'm sad to see that nobody gave another answer. I have another one that I think may be true, even though it contradicts my other one.
In thinking back about how I got saved, one of the things that happened was a breaking down of my preconceptions. One of those preconceptions was this one - that the God of the Bible is inconsistent and amoral.
My mind was changed on this subject before I did finally give in and turn to Christ. My mind had to have been changed, or I wouldn't have turned to Christ at all.
For me, personally, the breakdown became as I looked at children and their parents. Parents often give their children restrictions that the children think are "mean".
Example: My son, Joseph, once called me a big meanie because I spanked him for running out into the highway. He'd snuck out of the house and I saw him just as he was walking up the ditch to the highway and by the time I got the four feet from the window out to the door, he was actually in the road. I was terrified.
Now, say what you will about spanking, he got one because I would rather have him afraid of another spanking than to have him not remember the lesson that he is not to go onto the road. That may be mean, and plenty of people may think that spanking is cruel, but I love him and I would rather be cruel and save his life than be gentle and lose him.
I also teach my kids not to fight, to turn the other cheek, and all of the things we are supposed to teach our kids.
However, I also tell my children that if they are being attacked, and they have to fight to defend themselves, that they need to fight back, and fights as hard and as dirty as necessary to protect themselves. They're young, but they understand the difference between punching someone because they said "Star Wars is for babies" and fighting back when retreat isn't an option, or if you're facing a bully that must not be submitted to.
Some might say that this is inconsistent. I'm teaching them not to fight in one situation, and I'm teaching them to fight in another.
I don't see it as inconsistent at all. I see it as teaching my kids to be kind, patient, forgiving, and loving, while not expecting them to risk serious harm to themselves. In other words, it's about protecting them while ensuring they are not someone the world needs to be protected from.
Looking at God's "inconsistency" and "cruelty" in the Bible (as defined by these people) I see a God who sees the nation of Israel the same way I see my children. When God told them to kill each and every person (in my other answer) He was aware of the fact that the people from these other nations would corrupt His chosen people. He was acting out of love for His children.
He, unlike me, is omniscient. He did what was necessary to protect not only Israel, but everyone who would later be saved through Israel. And He acts towards them (and us) the way a loving father does to his children.
So as an amendment to my original answer, if you can get past some basic objections, and you have someone whose heart is not dead-set against the God of the Bible, then it probably is possible to show that God is a consistent moral lawgiver. (Because He is.)
And you'll have a easier time doing it if that person has children. It's so easy to show how God's love (and anger) is similar to the love and anger a parent feels for a child. It's something any parent can relate to.