Instead of writing angrily about anger once again, I'm going to lay down my personal sword and attempt to pick up God's. If I can throw off my own baggage and look objectively at Scripture, I think I will be much better equipped to deal with my own anger as well as others.
The Bible does not use the phrase righteous anger. It never prescribes anger, and it never says an angry response was good. The only thing in Scripture that comes close is Paul's instructions in Ephesians 4:26,
Be angry and do not sin; do not let the sun go down on your anger,
So you can be angry and not sin. And the way to be angry and not sin is to DEAL WITH IT quickly, before the sun goes down. Note that this does not say you must deal with it and settle it with whomever you are mad. Otherwise, it's an impossible standard because it would be utterly dependent on the cooperation of someone over whom you have no control. I used to think that if I was angry at bedtime with my husband, I HAD to talk it out with him before we turned the lights off. He did not hold the same opinion, and often was not nearly as mad with me as I was with him. And when he didn't want to talk, that made me REALLY mad. He was forcing me to sin, or so I thought. It's taken a while, but I've learned that I can well deal with my anger without my husband's help. In fact, I really must. He and I can talk about the issue underlying my anger once I stop being angry, but it's never once worked for us to talk about it while I am angry.
So far, we've read that the Word says that if you are angry, do not sin. Deal with your anger before much time passes. That passage in Ephesians ends with a discourse on forgiving others as God has forgiven us through Christ. But how do you get from point A (raging anger) to point B (forgiveness)? Thankfully, we do have an outlet for our anger. It is God Himself. And He has left us many examples in the Psalms of believers crying out to Him in their anger and frustration.
Psalms 73 gives us an example of a guy who is vexed at the wicked.
12 Behold, these are the wicked;
always at ease, they increase in riches.
13 All in vain have I kept my heart clean
and washed my hands in innocence.
14 For all the day long I have been stricken
and rebuked every morning.
16 But when I thought how to understand this,
it seemed to me a wearisome task,
17 until I went into the sanctuary of God;
then I discerned their end.
The Psalmist is frustrated about legitimate sins. Why are these evil people prospering?! He takes his vexation to God Himself, and God meets him in it and transforms him.
Consider also Psalm 10.
v 1 Why, O LORD, do you stand far off? Why do you hide yourself in times of trouble?
And Psalms 42.
v. 9 I say to God my Rock, "Why have you forgotten me? Why must I go about mourning, oppressed by the enemy?"
If God didn't give me these psalms in His inspired word to instruct me, I would never have thought it OK to bring such raw hurt to Him in prayer. Yet, in His mercy, He invites me to pour out my raw emotions to Him. While much of my anger is caused by my own selfishness, some of my anger is legitimately caused by other's sins that deeply wound myself or those I love. I must pour out my frustration, my disappointment, and my fears to someone. And God tells me that, in Christ, I can boldly and confidently pour it out to Him. THAT alone is my hope for transforming it from anger (which God says in James absolutely will NOT accomplish anything righteous) to some other emotion or resolve that God can use for His kingdom purposes.
The great justification for righteous anger is Jesus' cleansing of the temple. We Christians love to go all angry-Jesus-on-the-temple. But here's the problem with that. We don't attempt to forgive other's sins like Jesus did. We don't attempt to turn water into wine or raise the dead back to life. There are a whole string of things Jesus said and did that we do not do ourselves because they were things that were evidence that JESUS WAS GOD. Jesus was Lord over the temple. You and I are not. We are infringing on things that are only His as God when we use His cleansing of the temple to justify acting out on our anger. Again, think through why you would not tell someone that you are forgiving their sins. What is the difference in telling someone that you forgive them of their sins and, say, washing their feet? Well, one Jesus did to show He was God, and the other He did to give us an example of servant leadership. That's the same difference between cleansing the temple and turning the other cheek.
In summary, Scripture teaches that the only righteous anger is anger that is not exercised. The only outlet for righteous anger is God Himself. The only righteous actions that stem from anger are those that come out of the other side of the sieve of God Himself—vexation poured out to Him that He transforms into something else (resolve, burden, compassion) that He can then use for His kingdom.