How to get rid of gophers in the back yard without poison?
I'll echo @shirlock homes and ask for clarification if you are dealing with gophers or moles.

I'm not sure about gophers, but critters like moles will often burrow and tunnel into a yard because the yard is infested with grubs. They're there to eat the grubs. To get rid of the moles you then treat the grub problem and the moles go away.

Check out your yard, look for grubs and other insect infestations.