7 month old exhibiting typical signs of new teeth coming. He already has bottom 2 front teeth. How many nights in a row is it ok to give baby tylenol (acetaminophen)?

Teething. Acetaminophen (tylenol) should not be given more than 5 times a day nor for more than 7 days in a row.
Try non-medications. My preference is to try non-medication methods as much as possible. Teething rings or, taking a washcloth, moisten it, and put it in the refrigerator to get it cold. When your child is fussy, take it out of the fridge and let your child suck or chew on it. The coolness of the teething ring or washcloth will be soothing to your child's gums.
Depends. If the teeth are additional front teeth, they should cut through fairly quickly...The back teeth (molars) will take longer. You can cut back on some of the tylenol (acetaminophen) by trying other measures. Traditional cold teething rings work, there are also the teething sacks (which you can put cold fruit into) which children seem particularly fond of. You can also try some oragel over the counter.