What can help my maine coon cat who is often trying to cough up furballs.

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Of course, I love all cats, but I do have a special affection for the Maine Coon!  Look at this guy:
Not only are they large cats, but they also have very long hair, which makes hair balls  more common in them!  SO, glad you asked.
First of all, if your cat is vomiting more than once, maybe twice a month, that is not normal.  If there is hair in the vomit, that is ok, because most cats will have hair in their stomachs from grooming.  Hair in the stomach should normally move right through with food, but sometimes it gets stuck or balled up therefore, called a hairball.  Of course, that would be too simple for the scientists, they had to go and give them a crazy name like trichobezoars. The hair  really should not get stuck, however, but when it does, it becomes irritating to the stomach lining  which makes them naseous and vomit.  If they get large enough, they can actually block the stomach outflow.  Sometimes they are so big, they can get stuck in the esophagus on the way up when the cat vomits. OK, enough of the gross stuff...
If you think about it, throughout the ages, cats groom themselves and most do not have problems with hairballs. So, although there are products that are greasy promoted to help the hairball go down, that is really not the solution (and, they don't work).  The underlying problem is usually associated with motility or motion in the stomach, moving the food and hair out into the small intestine properly.  If your cat has frequent problems with hairballs, there is a medication that helps increase the stomach motility to help things move through better... however, getting to the underlying cause is sometimes a problem.  Please discuss the issue with your vet. If your cat has underlying inflammatory disease of the stomach wall or small intestines, the motion of the stomach changes and cats will vomit frequently.  Not much helps eliminate hair balls- but decreasing excessive grooming in a pet with known problems or even shaving them down can be done to decrease the likelihood, but again, that is not getting at the underlying problem, which is often gastrointestinal motility. Hairball remedies like laxatone and pineapple juice are not helpful... not sure if i have been either... but I hope so.  Good luck!