It might be unpopular to say it, but IMHO if they just legalized drugs, and regulated the sale of them like alcohol, this problem would probably die. Not to say that everything will be absolutely hunky-dory here... but the benefits will probably outweigh the costs. It'd be nice to see funding for Al-Qaeda and FARC dry up quite a bit. God knows neither of them need any more money.
If that seems unfeasible, perhaps just legalizing Marijuana would help. It's the no.1 used illegal drug (probably for the world, definitely in this country), it stands to reason that it would at the very least put a big dent in funds, and they do seem to be pushin' it (Al-Q at least, but FARC wouldn't surprise me)...
One thing the Taliban were good at was stopping opium production in Afghanistan. Since we defeated the Taliban opium production has gone through the roof - the people there are poor farmers and they are going to grow the crop that makes the most money.
Sarcasm