You could salt it.....it will kill what is there and won't let anything resprout for quite some time. salt in a yard fertilizer should work.

And then how about using a pre-emergent on it so that new seeds don't sprout?

Salting it sounds like a good idea, but there are a dozen Queen palms lining the drive. I'd be worried the salt might not be good for them as it leaches into the surrounding soil.

Echo,

You are in luck as Queen palms are moderately salt tolerant. While it may sting those roots that are under the driveway most of the roots won't be where the salt is.

For what you want to accomplish and with the guidelines you set you have very limited options. If it was me I would salt it...if that is something you don't want to do than hire a day laborer or a HS kid to remove the dead stuff after the roundup has done it's thing. You will just have to reapply the round up now and then but the weed problem will diminish over time.

If you decide on the Roundup route, you might try Tractor Supply. They have generic glyphospate 41% solution - 2.5 gallons for $50.

@bamboo rabbit: Thanks for the info about Queen Palms. But one more question, being from New England, I know salt is bad for dog's feet, and I have two large dogs that do walk up and down the drive (squirrels hang out in those Queen Palms). I wouldn't want to put out anything that would burn my dog's pads. Is there a particular salt I should use?

Echo,

Not to sound flip lol but salt is salt. The only difference is purity and size of the particles. I would use cattle salt from a feed store as it will drop out of a spreader and will be cheaper than using something like solar salt. you don't need to put it on so thick that the dogs are walking on solid salt. You want the salt to drop between the shells and get to the roots. We have a brick walkway and I salt it every year so nothing will grow in the cracks. Your project though sounds much bigger:)

As shuffles said if you go chemical go generic on the roundup as it is all the same chemical..I just always refer to the stuff as roundup. Adding ammounium sulphate to the roundup will make it work even better.