I'm sure there is much more than what I've found, but I have found the following, recently:
Mom's BBQ Pit is at 611 St George Ave (corner of Chestnut) in Roselle. The owner (Mom?) is Brazilian. I don't think that this qualifies as a bbq pit in the Southern sense, but the chicken and ribs were good. I got mine without sauce, and they were tasty. You can get black beans and rice, too. Take-out only.
In Elizabeth, at 537 Pennington St off of Elmora Ave is Elmora Barbecue and Lunch. Didn't have room to try anything (please don't kick me off the board, Jim ), but there were chickens and other things grilling on spits that looked quite good. Several members of the local police force were eating there, fwiw. I don't know if that means the food is good, or just that they don't have to pay. Looked good though. They even have grilled quails. I believe this place is Portuguese. As you can probably tell from the name, it's a bit of a dive, but since when did that stop anyone?
Just up the street on Elmora Ave are a number of places. Burgers 'n Bites seems to be Israeli. Monserrate is Colombian.
Of course, continuing up Elmora one gets to Fritz's butcher just around the corner from Keane College, but I've already mentioned that place.
Anyone familiar with this area, or other parts of Elizabeth?