Burying bones will leave you open to animal cruelty issues if for some crazy reason someone else found out about it. An anonymous call to "which ever" city department handles the regulations for burial of pets is advised.
Cremation is a step I have suggested to others too
I agree with my colleague - call animal control and ask anonymously.
Depending on your backyard set up, you may want to think twice about doing this. I won't get too graphic, but if you have any wildlife (coyotes, raccoons, etc) your pets may not stay buried. You may want to think about cremation. Animal control can give you phone numbers for local pet crematoriums.
My family buried our deceased pets in our backyard when I was growing up, although that was another time...while I have not heard of laws prohibiting what you ask about I can imagine some towns having such an ordinance. Call your local animal control to inquire whether or not any such laws exist in your area.
Personally, I have gone the cremation route with my own pets since I have been on my own, but that also incurs expense that may or may not be a burden. And, my colleagues have good points to make about backyard burial beyond the legalities. It is not an easy decision to make...but I do recommend checking with your local officials to see if there are any local laws regarding this, and also check with veterinarians regarding the cost of cremation, so you can at least be sure of your options.
(THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.)