Any of the weedkillers mentioned willl do the trick ... Getting the stuff to stay gone on a permanent basis is the trick though. Note that the fine print says "Up to a Year".
I've been battling a deeply dug in crop of Poison Ivy since I bought my house, each summer I gain a little bit more ground, and I think I may finally have beaten it last year ... After blasting the site with Roundup and letting that work for a few days, I waited to see what I'd missed then hit it with a second treatment, just to get all the survivors ... After letting that work for a few days, I tacked heavy black plastic tarp over the entire area ... This did two things, it blocked the sun completely, and worked as a heat trap to make the ground very hot ... this cooks anything left living underneath and basically scorches the area you're trying to clear of life. As soon as the frost clears this summer, I will be covering the area with landscaping fabric and mulch to discourage any new growth.