Why not sit with the dog in the sun with a drink for both of you, while you review the Dhamma you have learned for yourself in a calm voice? Stay in physical contact with them for a time. If you hug them, as a habit, they can feel you speaking even if they can't hear it, which can comfort some animals.
I think these sorts of things may be helpful for both beings. Chanting really loudly, maybe less so.
It's a difficult spot. I've only ever had pets die while as a child, and my parents took them to the veterinarian for euthanasia. I have avoided having pets since living on my own, partly due to this sort of thing.