Ditto...
If its already suckering you may have to use several applications to kill it completely by just spraying the regrowth. I would recommend cutting the stump fresh to ensure best results, also score through any exposed roots and apply herbicide to them also, not just the stump, these things have 9000 lives!
If you can get it, Tordon R.T.U is very effective on pepper, but DO NOT use it if the stump very close to anything you want to save.
Read the labels and decide what level of risk you can take!
BTW, if you have the time and patience you can kill the stump by just bashing off any new sprouts every time they re-appear, eventually the stump will starve and die without chemicals...