What about this idea from a Zoo?

[Mups]

I was thinking of cats and dogs Mups, watching a horse drop to the floor is something I couldn't face I'm afraid. It may be traumatic for us holding our pet when they're put to sleep, but I go along with the vet's experience on this that it's less stressful for the animal..

Yes,  I agree too.
I wouldn't dream of leaving a dog of mine at a time like that.

[muddy]

I have always buried my pets .

[Mups]

I have always buried my pets .

I think that idea is fine as long as you intend to stay in that house.  Not sure I could manage to dig a deep enough hole now though,  especially with the drought we've had this year.

I have only buried one of my dogs,  the GSD in my avatar, Elmo.
I buried him at the bungalow where I used to live,  and planted some flowers and shrubs on his grave. 
Only thing is,   it upset me so much when I moved here and had to leave him behind.   So I dug up the Rhododendron and brought it with me,   Still have it to this day and it gets bigger and more beautiful every year.   
It also worried me about new people moving into my old bungalow,  in case they dug him up.
I have had the ashes back of my dogs ever since.

When I lived on the farm, I used to bury and poultry or goats though.

[Alex]

My dog and 2 cats are buried in the garden, the last cat I had cremated so I've still got her ashes.

[Michael Rolls]

I had Fleur cremated. Put some of her ashes in Veronica's grave, some at the base of her favourite tree in the park, some behind the bench on her nearby walk, and the rest are in a lovely container with her name on it in the kitchen