Walk me through your process, from brine/marinade to finish. I’m talking specifically about drumsticks and bone-in thighs. I can never quite seem to nail it. I usually end up with an over charred exterior.
I have a single zone Weber, so, cooking with indirect heat is out, which works against me.
I rarely do it but I marinate in something like vinegar and spices for at least six hours. If your marinade has sugar in it that may be the problem. Take them out of the fride AND the marinade an hour before I want to grill them. Grill them in batches on one side of the grill about 6 to 8 minutes each then set them on the other side to finish while cooking the other batches. Constantly monitoring and moving them and use a digital thermometer to check them.
Leave the skin on, sprinkle a med/heavy dose of Lawyre’s season salt on both sides of both thighs and drumsticks. Place on a 3 second fire, turn over every 3-4 minutes for 45 minutes or until cooked through. Rotate around the grill as hot spots emerge so you don’t char/blacken the skin. START WITH THE BOTTOM DOWN, in case of a hot spot so you don’t crisp the skin in the first 4 minutes. Also works with breasts but they usually need a few more minutes to cook. 5-10 more. Best damn bbq chicken ever. You’re welcome 
Edit: the skin will get crispy - it shouldn’t be soggy, more like a nicely toasted skin, just not black char.
2nd Edit: trim the skin on the thighs. I’ve found they usually have a massive amount of extra. You jus want enough to cover the meat and still be attached.
Wait are you talking full size or the buffalo wing size?
Full size.
I think sugar might be the problem as my brine contains OJ. Also have been going direct from marinade to grill.
You need to cook with indirect heat. 
Can you move the chicken away from the hottest part?
I don’t marinate my chicken. If you watch the temperature you won’t dry it out.
As to seasoning. I season with kosher salt, Weber Roasted Garlic and Herb seasoning and Everglades Cactus Dust. I use all three. My chicken turns out really good. Though I do use indirect heating and a digital thermometer to let me know when it hits 160ish.
For whatever reason, chicken breasts are super simple for me. Flatten them a bit and brine them and you’re 95% of the way there.
I usually make them in a smoker, but you could do it in a weber with some wood chips.
Baste with olive oil and sprinkle with Buffalo Wild Wings salt and vinegar rub.
270 deg for 2 hrs, turning after one hour.
No sauce needed.
Dang. I forgot the wood chips until I saw J-No’s post. I use hickory and one piece of mesquite.
The key for the drumsticks and thighs is constant turning and supervision. Setting a timer and being right there with a fire that’s not too hot not too cold! It helps to have a nice cold beverage close by too. We also put the lid on with some vents for air flow.
You can do indirect heat with a Weber. You just need the right insert to hold the charcoal.
Full size.
I think sugar might be the problem as my brine contains OJ. Also have been going direct from marinade to grill.
Sugar burns and if you don’t take it out then it takes longer to get the internal temperature right meaning more chance to burn
You can do indirect heat with a Weber. You just need the right insert to hold the charcoal.
It’s a Weber gas grill, one of the small clamshell types.
2 burners, 1 zone.
Are there flavor bars or something that you can set a metal pan on to deflect heat away from the meat? Or, you can man up and buy a Weber Genesis 3 burner grill.
The most important thing to have is a thermometer so that you can monitor the temperature of the meat. A couple of years ago I discovered AmazingRibs.com website. They emphasize using some type of thermometer to make sure you don’t over/under cook your meat. Since applying their principals my grilling and smoking has gone up several notches.
I just checked out amazingribs.com.
Thank you. Thank you so very much kind sir!
I just checked out amazingribs.com.
Thank you. Thank you so very much kind sir!
Glad to recommend them. I’ve met several people who have talked about how much that website helps.
Good luck with your meat. Oh, that was someone else with that problem.
You can do indirect heat with a Weber. You just need the right insert to hold the charcoal.
It’s a Weber gas grill, one of the small clamshell types.
2 burners, 1 zone.
See, that’s not a real Weber. That’s just a gas grill.
Get a proper kettle grill.
If you’re going to grill with a single-zone gas grill, might as well use your oven. Preheat to 500, let it sit for a bit, put the legs on racks, marinated dry rubbed, whatever… into oven - after 10-15, take a look, skin should be crispy, tun off ovn, leave oven door closed let them cook through for another 25-30. Should be juicy with crispy skin. I cook a lot of meats in the oven this way after reading Alton Brown.
For grilling and the requisite taste, gotta use charcoal. Sear, move indirect. But it appears you knew that.
Sprinkle with Tony Chachare’s
Grill over medium heat for 25-30 minutes, turning often so the skin doesn’t burn. If they start to flare up, move them off the flame.
If my parents are coming over, I’ll brush some BBQ sauce on them in the last 5 minutes, they love that shit. Not me.
I just checked out amazingribs.com.
Thank you. Thank you so very much kind sir!
I forgot to mention something. Amazing Ribs has several great recipes for rubs and sauces.
Memphis Dry Rub - I put it on any pork that I smoke.
Simon and Garfunkel - I spatchcocked a turkey (their advice) and put this rub on it. It is by far the best turkey (except for maybe fried) that I’ve ever had. The spatchcock makes a YUGE difference as the white meat doesn’t dry out and all of the skin gets crispy.
Carolina Mustard BBQ sauce - I grilled some wings and then put this on it for the last 5 minutes. It produced my best wings ever. My wife, daughter and father all talked about the flavor.