I hate to disagree with Eric, 'cause he really knows his stuff, but I think a 30.06 with a night scope would be a better choice. With a shotgun, you chance killing beneficial insects, too.
"Imagination is more important than knowledge." -- Albert Einstein
Stinkbugs get out of hand pretty quick, and hand-picking is probably the best solution for me. I kill at least 5 per day while harvesting - especially on the okra. If you can find the eggs before they hatch, that's always helpful...Here's a pic that I took a while back, just for reference....
Stink bugs are hard to control. Even birds seem reluctant to eat them. Here is one suggestion I found.
" you can try scattering kaolin clay around the area, or spray your plants with a kaolin clay solution. Stink bugs are not able to lay eggs and feed on plants covered in this harmless mineral clay, which can simply be washed off any vegetables and fruits.
If you're lucky, your stink bugs will be attacked by predators and parasites. A number of organisms will attack stink bug eggs, and while these organisms are not available for commercial sale, they may be present in your area, especially if you live in an agricultural community. Many state-sponsored stink bug control methods have focused on the release of such parasites, protecting crops and gardens in the areas that they are released.
If these measures do not work, a number of companies produce organic insecticide soaps which are targeted at stink bugs."