I love the fact that you can buy chicken legs and thighs for next to nothing. I always have a lot of them in the chest freezer, three to a freezer bag. This is the best way I know how to cook them on the grill. Everyone loves the crispy skin and the process requires no watching at all.
Make sure chicken legs and thighs are thawed all the way through. Start the grill and let it get to 500 degrees. Charcoal users just let it get as hot as it will get. You can't do this on a grill without a cover. It can be done in the oven but the results are just not the same. For an extra touch soak wood chips in water and put them in a smoking box and place over one of the burners that you leave on. That will give enough smoke flavor to the chicken to make it really good.
Sprinkle blackening seasoning and jerk chicken spice evenly on the skin side of the legs and thighs only. Spray with non stick spray so all skin parts are covered. You can do this with oil too just not extra virgin olive oil.
Turn off one burner of the grill. This should reduce the temperature in the grill to around 360. If it doesn't adjust the remaining burners to get to 350 or 360. If you are using charcoal move the charcoal to one side of the grill. Place the chicken legs and thighs, skin side up, on the grill over the part where the fire is turned off. Close the lid and cook for 45 minutes. Don't turn over. The skin will roast nicely and get a beautiful golden crispy. You will have to watch them if you are using charcoal.