Heres what I found on Halachafortoday.com
256) Q: Is it against halacha to euthanize a pet? Our cat is 19 years old and is simply dying of old age. The vet gave us a list of sicknesses she may be suffering from but there is no cure at this stage of the game for any of those possible problems. I have been under the impression forever that it is against halacha to euthanize an animal. A close relative (who knows how to learn) claims otherwise and is urging us to put the cat down. Is there a heter to do this?