To find rescues that work with dogs like yours,
visit www.petfinder.com. Put in your dog's breed(s) and your zipcode (as if you were adopting a dog), and petfinder will find rescues within a 25-50 mile radius of you.
To carefully rehome a dog yourself:
(1) Always ask potential adopters for the phone number of their veterinarian, then call the vet's office for a reference. You'll find that most vets' offices are very helpful! This is the BEST way to quickly eliminate irresponsible pet owners and creeps who acquire animals for dog fighting bait, laboratories or feeding to their snakes. (YES, this happens!)
(2) Copy the adoption application of any good rescue and ask potential adopters the same questions.
(3) Post pictures of your pet at all vet's offices, together with a description of their qualities and needs. Don't lie about your pet's faults (and be willing to recognize that some of these faults might be your own, if you haven't provided good, consistent leadership and training).
(4) Be prepared to update your pet on all vaccines and lab tests, plus neutering, prior to placing.
(5) Request that potential adopters bring pictures of previous pets and their home if you're not willing to visit their home directly. Check their address at googlemaps.com and review their profile on Facebook before meeting them!
To get practical, easy-to-implement behavioral help for most dog issues that requires NO trainers and NO lesson plans (only a greater understanding of canine body language and how to better use your own, plus how to create routines that fulfill your dogs' needs as well as your own, check out THIS inexpensive book).
Considering reliquishing your dog?