Smoked a chicken and the skin came out like boot leather

Take cheesecloth and soak it in melted butter and drape it over the bird before you put it in the smoker. This will protect the skin during the long slow smoking process. You may want to pull the cheesecloth off about 30 minutes before you are done. This will give you a nice golden brown skin that is not leathery.

I first read of doing this with a smoked turkey, but tried it with a chicken and it comes out great.

First thing I would recommend is not spraying down the skin with the oil/apple juice mixture. There is plenty of fat in chicken skin. No need to add more. And spraying the skin will just keep it from rendering out the unwanted fat and other tissue, thus preventing it from crisping.

The other thing I would suggest is to turn the heat up on the chicken. Low heat + smoke = rubbery and tough skin. I do a lot of barbecue, and I never find any compelling reasons to do chicken low and slow, unless I want to make pulled chicken, at which point the skin is useless to me anyway. I prefer to make chicken in the 325f range, as it turns out much better skin at that temperature. You can even get away with cooking at a lower temperature, then cranking the heat up to finish the skin.

Finally, I would suggest ensuring that the surface of the skin is very dry, and has been salted (not heavily, just a bit), before putting it on the cooker. This, too, improves skin texture.

The TL;DR version:

1. Quit messing with it while it's cooking.
2. Turn the heat up.
3. Dry and salt the skin before cooking.

225-250 is too low a temperature for chicken. Chicken doesn't benefit from "low and slow" cooking, because it doesn't contain connective tissue that needs to be broken down, and the skin needs a higher temperature to crisp.

Here is a page from Virtual Weber Bullet which talks about how to get a crisp skin while smoking. They recommend cooking at 300 degrees F.

I can confirm that hot & fast is the way to go. I just smoked my first chicken using advice from this thread, and it came out perfect. Our guest said it was the best chicken she had ever eaten. Specifically: Pellet grill set for 350. Chicken spatchcocked, coated with olive oil, and rubbed with Lawry's Poultry rub. Roasted with remote thermometer in breast to internal temp of 165. Didn't open the grill till it was done.

Chicken breasts don't benefit from low and slow. Try using a brown sugar rub on skinless thighs and smoke for 3 hours at 225F/107C. You won't care about skin after you taste that.

I actually did the low and slow to allow the meat to absorb the smoke while slowly cooking to correct temperature. I changed the temperature up and down 220-300 to allow for 3 hours in the smoker without over cooking. I stopped the smoking in the 155 degree area to allow me to put on direct flame. It even flamed up to the chicken giving me the slight char and crispy skin we all want.