This may sound harsh to some, but I recommend taking the most personal yet dignified course of action. Put the animal down yourself.
It is bad enough that the poor animal must suffer with the cancer, why make it go through the cold-hearted indignity of having some un-caring stranger inject it with poison?
This may be hard for you to swallow, but I think if you consider this idea, and your own psychological well being, you will come to the conclusion that this way is best.
Many years ago, when I was a teenager I had to put down a family dog of 11 years. No doubt it was a very difficult thing to do. But in retrospect, I do not regret the action I took, and I have the psychological comfort of knowing that my dog went out in a respectful, loving, and dignified way.
[soapbox]
[PS FYI to all, don't bother asking for more details.]