Question to you: What do you do as a citizen of the US when you know that there is a man out there terrorizing children? What action can you take?
There was a great interview with a warlord in Afghanistan on NPR, where he basically said, "You can bring voting to my country, you can tell us one man one vote, but our clans are more important to us and no person will ever vote against their clan, so every election will still be decided by who has the largest clan." He went on to explain that this is de facto how things work already, except instead of bothering with a ballot they just check to see who has more men willing to fight, and only if there is a disagreement over who would win do they actually fight it out -- which will still happen with elections, if the person with the bigger army disagrees with the result.
Africa is kinda that way -- we give money and feel good about it, but most areas of Africa have a culture in which resource appropriation is the accepted way to gain dominance, and only a very few organizations (for instance, Peace Corps) effectively administer aid without it just propping up one or another faction that inevitably turns violent. That doesn't make Africans in any way lesser or uncivilized as some racist, xenophobic assholes would suggest; it's just exactly the cultural traits one would expect from an entire continent that has been characterized for thousands of years by being an extremely dangerous place to live. Europeans have no significant cultural memory of experiences like not being able to go outside because something might eat you. For Africans in many parts of the continent, that's not even a cultural memory, it's a frequent reality. The book "The Poisonwood Bible" presents a good (fictional) account of how impossible it can be for most non-Africans to really understand that.
So back to the economic development thing: Giveaways just get appropriated, but increasing individuals' ability across the board to produce their own food and other resources seems to work fairly well. And if you don't give away resources, but give away knowledge and require a reasonable-for-the-area investment to get resources, governments and militias don't have an incentive to steal -- they are usually well funded enough to have access to knowledge already, and they aren't interested in buying something they can't use for a fair market value. I have a personal friend who has sold me on the org he works with, IDE: http://www.ideorg.org/ They develop technology that can increase output for self-sustaining farmers in developing countries, giving them the opportunity to produce more than just food for their own families, which means for the first time they will have something to sell, which means capital to spend on things like medical care and education.
Despite the desire of my bleeding little heart to recommend something less Rand-ish sounding than a "charity" that SELLS things to poor farmers in Africa, I have to say, you can't really argue with results that are almost impossible for miscellaneous militias and warlords to steal. If everyone in Uganda had a thriving home business and adequate capital, I don't think people like Kony would ever gain a footing -- someone with their own shotgun would have put a bullet in his head the first time he kidnapped a child on their property, and villages terrorized by militias would raise their own local police forces.
As far as the short term, I'm not sure there's anything that can be done about the bastard that's not already being done by the US government and international interests. And, to be fair, these filmmakers and their 11 movies may have helped to bring that about. I don't really know, but it's entirely possible. You could give money to that guy who's running a one-man manhunt for Kony, but he seems a little shady himself, what with the arms dealing and all. You could look into adopting a child from Uganda -- "Might not change the world, but it would mean the world to one child," and so on and so forth. You could look for a Peace Corps project in Africa to support; my cousin recently returned from a two year tour in Lesotho, and recommends wholeheartedly the work the Corps is doing in that country. You could send a handwritten letter (so rare they get read; form letters just annoy interns) to your Congressman and his opponent if any, saying that you will vote for and donate to the candidate who gives you the most convincing response as to how he plans to advocate for a solution to child conscription in Uganda. Or, you could just cross your fingers and hope my suspicion here is just a function of knowing one too many "filmmakers" with the same cowboy mentality about third world countries--I could be completely wrong about these guys, after all.
It's not an easy issue and like most things worth while, there isn't an easy fix. I wouldn't be surprised if these video's did have something to do with the US's impetus to go after Kony.
You mention supporting a "child" in Uganda. Since you seem to have some knowledge in this area, do you know of a reputable program for such things? I'm definitely interested.