Use cuttings from semi-hardwood stems for propagating the sweet olive, suggests the Texas A&M University Extension. Semi-hardwood cuttings are the current-year growth; they're not very supple but still not as hard and mature as hardwood cuttings. The best time to take semi-hardwood cuttings is after the active growth period has slowed, between summer and fall.
Cut 4- to 8-inch-sections from healthy, semi-hardwood stems from the sweet olive plant. Use sharp, clean scissors and measure from the stem tips. Remove all leaves from the lower half of the stem and leave a few leaves at the top. These leaves continue to produce a substance that will help with the production of roots, according to the Washington State University Extension.
Fill a medium-sized pot with equal amounts of peat, perlite and sand. Fine gravel also works well instead of sand. Dip the base of each cutting into a rooting hormone and plant immediately in the rooting medium, inserting each cutting to a depth of 2 to 3 inches. Water well and place the pot in a large, clear plastic bag. Close top and place in a warm, bright area out of direct light. Water every three to four days with enough water to keep the medium moist. Cuttings generally root within a few weeks.
Plant sweet olive in an area of full to partial sun, preferably a site that has shade from the afternoon sun. The plant adapts well to a variety of soils except the very infertile or sandy types. Sweet olive has an average water requirement and is hardy in USDA zones 8 to 10. Scales are among the few pests of sweet olive and are often seen on plants that are growing under poor cultural conditions.