The fence idea of digging a trench and putting stones in is a great idea... except it's Arizona... dig 2 inches down and you hit rock. Once I finish the gate, it should deter the rabbits some... if not I shall be giving the trench digging a try.

I actually couldn't dig the garden out, I had to build it up over the last year and pull weeds out because without a machine to dig through the soil there was no way I would have been able to do it by hand in time.
We have quail here, pigeons are not usually around here, some doves, crows, etc... the quail are so used to us they literally stand there and stare at us like we're crazy. We hung plastic bags from the fence which blow and make noise, doesn't seem to bother them a bit. Will try stringing some bailing twine from poles and hanging things from it to scare them off.
The are the potatoes are in is a new area, have never planted them there before. Have been down on my hands and knees crawling through the rows and cannot find one worm or bug on them, so I am thinking they are in the soil and come up at night maybe. At first they just had some holes in them (not like rabbits had chewed on them, just holes here and there through them), small ones, in some of the leafs...now, it's gotten to the point that there is nothing but stem left and the remaining leafs are being eaten away as well.
The tomatoes and peppers are in a mixture, the same as the garden... it has wood ash, compost, manure (horse, dried for at least 1 year, some as a long as 2 years), black dirt, and some organic potting soil. They are in those starter pots that decompose over time and allow the roots to grow through. They are on the back porch, so they have the morning sun until it passes over the house around noon and then they have shade, outside all the time (were in the house, but the cat tried to eat the sprouts). They also get watered either once a day if needed, basically when all the water has been soaked up and the pots are beginning to dry (we water from the bottom as the pots soak the water up and moisten the soil all over). Heat? It's Central Arizona, was 93 F yesterday on the back porch, 97 today. They look like they are about an inch or so above the soil line, nice green color, but they've looked like that for over a month and a half now, just sprouts.
Thanks for the ideas!