You can try to get one through Great Dane Rescue Inc based out of Michigan and yes they check every aspect of your home and yard and check your vet as well They usually send out some one to check your home out and you cannot have any dogs that are intact at all for them to adopt out to you and your children have to be 8 or older if you have any. These dogs are very well taken care of.
Also you can try the local shelters, thing is the Great Danes are normally not there, they cal the rescues and they do normally pick them up first.
Also puppy mills or breeders I do not like so there is one in Indiana I know of that do have great danes and they are very good with their animals that is Dan lea farms off of st rd 39 and I-70.
Great danes are not like a normal dog at al and take special food and care and you must know these type of dogs as pups are very smart and they grow til they are at east 2 years old minimum.
If you have any questions about this my email is open as we have fostered great danes for 6 years and have 3 of our own. Please feel free to email me and I can hook you up if you want the right info