A dog poop hole is easy, just dig and dump it in there. But to make a hidden, aesthetic dog poop hole, do the following.
At the top of the hole will be a ring of paver stones without the center stone. Glue the ring together with construction adhesive. The missing center stone is the size of the hole opening.
Place the stone ring on the ground and dig around the perimeter so the stone ring lays flush with the ground so the lawnmower clears it. Remove the ring and use a posthole digger to dig a 3 foot deep (more or less), pear-shaped hole.
Put the stone ring back and cover the opening with a flat stone that you can kick aside when you dump in the waste.
The 3 foot hole lasted 1 ½ years for my 70 lb. dog.
When you dig a new hole, put some of that dirt over the old hole, level it, and the hole is gone. If the new hole is on the lawn, the grass I cut out is place on top of the old hole and it fills in quickly.