Tap four to six 4-foot tall, steel T-stakes with hooks into the ground around the cherry bushes, surrounding the entire group of bushes with the stakes. Insert the stakes no farther than 2 to 3 inches deep by using a wooden mallet.
Drive the stakes farther into soil by using a fence-post driver. Slide the driver onto one stake, and pump the driver's handles downward to force the post into the soil. The stake must be more than 6 inches deep in the soil. Repeat the procedure for each other stake.
Dig a 6-inch deep trench around the cherry bushes, following the stakes' perimeter. The trench will prevent rabbits from tunneling beneath the protective fencing you will install.
Place the bottom edge of 3 1/2-feet-tall chicken wire fencing into the trench while unrolling the fencing around the stakes. Slide the fencing onto the stakes' hooks where possible. The chicken wire fencing must have 1 inch or smaller holes because young rabbits can fit through remarkably tight spaces.
Cut the excess fencing where it meets the end of the fencing you installed first, using wire cutters for the task. Close the fence, connecting its two ends, with cable ties.
Fill the remainder of the trench with the soil you removed to create the trench. Bury the bottom of the fencing under the soil.
Clear area rabbit habitats, such as debris, brush and stone piles, to deter rabbits from staying in the yard.