Michele, my favorite method is covering with plastic, too. If you can seal down the edges of the plastic with boards, mulch bags, rocks or whatever to keep the air from circulating under it, it will work well.
But, sadly you will always have to be vigilant, because it seeds itself generously and the birds eat and spread the seeds. So you could kill every single bit of it, and it will still come back. Don't let this discourage you, we're all in this fight along with you.
