I had to have my dog put to sleep a few years back due to old age and medical problems.  My dog was always a little nervous at the vets and I didn't want his final moments to be in a place he wasn't comfortable in. 
I waited until I knew that it was going to be sunny and clear in a few days and arranged for my vet to come over.  I had a picnic in my backyard for my dog, he was surrounded all of his favorite toys and doggy treats.  The vet and his assistant showed up and gave him a shot.  He slowly drifted away as I hugged him and cried my eyes out.  Then the vet and his assistant helped me wrap him up in his doggy blanket and they put them in their van and took him to the pet crematorium for me.  
It was really hard to have him put to sleep but I was so glad that it was done at home and I know my dog was happy that his final place was there in a place he loved instead of the vets office.  
I can only hope that some day I go out in a similar way surrounded by my favorite toys, food and loved ones outdoors on a sunny spring day.  
Anyway, if your vet is unable to come to you I'd recommend calling around and finding one who will.