One of the big produces of methane (a greenhouse gas) is the livestock industries (farm animals). Cows, sheep, goats, pigs etc, produce gas through their digestive system. Here's an idea, although it would only help partially.
Peppermint, or even the weed like mint, is a well known herb for helping digestion and easing stomach gas and cramps. If you gave livestock peppermint or mint (very easy and cheap to grow) in their feed, maybe it could reduce gases. It would also reduce the incidence of bloating, bloating related vet bills, and help make a healthier animal.
You could grow peppermint, or mint, in the field, or add it to hay or grain feed, or feed it to them separately. In the wild, the animals ancestors of modern livestock had access to a lot of different plants. They would graze on a variety of wild, naturally formed grasses, and herbs, and nibble on bushes. Their diets were rarely a monotone of exactly the same plant day in and day out. Near rivers there were rices, on the plains were all kinds of grain grasses. Near forests or in heathers, marshes and plains were herbs and scrub which added to there diet's variety. I would almost guarantee that they ate certain things deliberately for certain conditions. Peppermint would almost certainly be one of those plants.
Observing their wild counterparts in a natural native environment to see what they do to ease certain health problems could lead to all sorts of possible natural cures for livestock health issues. If they nibble on certain bushes or herbs or vines for certain conditions, like stomach pain, gestation, wounds or whatever, growing the plants in paddocks (as ground cover or hedgerow) saves a lot of time and monitoring. You do not have to give the animal the cure, it just takes it as needed. Then, if further help is needed, the animal is observed, like a pet cat eating grass. Nurseries could benefit financially from selling the plants and farmers could save a lot of time and effort after the initial start up, and time and effort is money and health. Some plants grown as trees and bushes in hedges or as herbs could be extended as well as a cash crop.
Sheep and other animals that tend to chew cud, there is a lot of greenhouse gas burped up. In their stomachs and intestines there is a conglomerate of all kinds of interesting bacterias in a mini ecosystem of their own, hopefully balanced for the comfort and health of the animal. Here is another idea. With a little research, a (or a few) good bacteria for these animals, that produce less methane or bad gases, can be isolated, developed and grown for commercial reasons. Like pro-biotics. Then, the bacteria can be fed to the animals, the logical time being when they are lambs or at the milk feeding age. Current systems of economy that sell preventative medicines for livestock could benefit from it financially.
An interesting fact, incidentally, is that herbivores stand facing north while they are grazing. If you are lost in the country and need to know where north is, just look which way the grazers are pointing. That's north. It is a bit mysterious but probably has a very reasonable explanation to why. The how is probably magnetic. Maybe it has something to do with the sun or predators (of the past).
Cud - grazing animals who have more then one stomach vomit up food from one stomach, chew it again, and then pass it into it's next stomach.
Herbivores - animals that eat plants only.
Pro-biotics - good bacteria eaten for their beneficial effects on the digestion, like yogurt.