Are there any alternative treatments for dental halitosis?

Do you have GERD? Have you been dignosed with gerd? If it is related to gerd then follow the treatment recommendations. Alternatives treatments (pills?) may not help but i think eating fresh fruits and vege's and parsley leaves might besides proper daily home oral hygiene. If you let bacteria grow on you teeth and gums, they will produce the sulfur compounds that cause bad odors. So get soft tooth brush and floss.
Find the cause first. You need to find the cause first before you treat "bad breath" or halitosis. Most of the time a profession dental cleaning to remove plaque or tar build up (which leads to bacteria producing a sulfur-like compound that emits the bad odor.) Some mouth rinses can help but its temporary. Digestive problems, certain foods or some health conditions can also lead to halitosis.
Root planning. The most common cause of halitosis (bad breath) is inadequate home care and hygiene practices and not having a professional cleaning on a regular basis. The tissue around your teeth becomes inflamed and then progresses to a full blown chronic infection. The treatment is to have, at minimum, root planning and sub-gingival curettage by a dentist or hygienist and improved home care including flossing.