The discoloration (black) of the paws is caused by chronic inflammation and the inflammatory cells releasing melanin. In addition, the chronic exposure of the coat to saliva causes darkening of the coat. One of the most common causes for excessive licking of the paws is an underlying allergy (food or environmental). This is what I would recommend you try:
1- Need to stop the licking or will not get better. Pick up an ecollar (cone) in your local pet store to stop her from licking.
2- Soak her paws 2-3 times a day for 5 minutes in a solution of chlorhexiderm shampoo/soap. You can find chlorhexiderm over the counter in any pet store. Dilute 1 tablespoon of soap for every cup of water.
3- Once you soak the paws as above, dry and apply a topical antibiotic like neosporin or bacitracin.
4- Change the diet
to a prescription food called Hill's z/d or a grain free diet with a different source of protein then what he normally has in the past. For example: Taste of Wild Salmon. When on this diet he should not eat anything else or he will not improve. Needs to be on this diet for 6-8 weeks before you see significant improvement.
5- Start her on Benadryl (diphenhydramine) 1mg for every pound body weight every 12 hours. For example if he weighs 10 lbs he will require 10mg every 12 hours.
6- Supplement with Fish Oil, 20mg of EPA for every pound body weight once a day, long term.
7- If after doing the above there is no improvement, have her checked by your family veterinarian.
Hope the above helps, if you have additional questions I will be glad to answer them.