Cut 4 to 6 inches from several stem tips with leaves from a healthy rabbiteye blueberry bush in the spring or early summer using a sharp knife. Remove the leaves from the bottom half of each cutting.
Dust the cut end of each blueberry cutting with a rooting compound to promote root growth.
Fill a seed tray with a rooting medium such as perlite, sand or potting soil. Insert the bottom one-third to half of each blueberry cutting into the rooting medium in a cell in the seed tray. Water the cutting so the soil is moist but not wet.
Poke several holes in a large, clear plastic bag with a pencil to provide proper air circulation. Place the seed tray in the plastic bag. Seal the bag with the rubber band. Place the blueberry cuttings in a warm area with indirect light. Mist the cuttings daily with a spray bottle of water. Keep the sides of the plastic bag from contacting the cuttings.
Transplant the rabbiteye blueberry cuttings after they have rooted well and begun to produce new leaves. Plant the cuttings in 1-gallon grow-out pots filled with potting soil. Grow the plants outdoors to harden them until around 1 to 3 feet tall before planting them in your garden.