A year ago-ish, I was asking the same question. There is a thread here on Toledo Talk with some suggestions if you search for it.
Not sure if this is still accurate info or not, but Dr. Pifer at Countryside Animal Hospital in Sylvania said he could do it (419-882-7688) but it's not an on-call thing. You have to already be a patient and you have to be able to schedule euthanasia several days in advance, which isn't always the case. I would also suppose he may have limits, also, regarding how far he'd travel.
I cannot tell you how much it costs, because our dog ended up having a medical emergency and we were forced to euthanize with only a few moments notice, while he was already there at the vet's.
If we ever get another dog (and we will, some day), this will be one of the questions I ask when we are selecting a new vet, instead of waiting until he/she gets elderly/sick.
There is always another option. When you know your dog is approaching her time to go, you could ask your regular vet for a sedative to give her before you take her in that last time. It will make her sleepy and relax her.
Good thoughts to you and your dog.