Answer: Plum trees do sucker (send out shoots from the roots) and although you can cut these off, more usually sprout along the root system. I'd vote for a persimmon tree. They are attractive, don't sucker, and do produce edible fruit. Here are a few cultivars for you to consider:
Large, oblong-conical fruit Skin glossy, deep orange. Flesh dark yellow. Sweet and rich. Good for drying. Ripens midseason to late. Tree vigorous, upright-spreading. Prolific in California.
Small, roundish oblate fruit with thin skin. Skin and flesh ripen to a distinct orange-red. Very sweet and rich. Excellent for fresh eating and drying. Ripens midseason to late. Tall, upright, moderately vigorous tree. Bears good crop.
Small, elongated fruit. Skin dull-yellow when mature. Flavor sweet, excellent, ranked among the best by gourmets. Mature fruits are attractive when dried. Tree medium in height, bears consistently. Cold hardy to -10? F.
Large, somewhat four-sided fruit, broad-oblate and indented around the middle. Skin thick, orange-red. Flesh light orange, sweet and rich when fully ripe. Ripens midseason in California
Medium-sized round-conical fruits. Skin light yellow or orange, turning orange-red, thick. Flesh yellow, sweet. Ripens early. Tree vigorous, rounded, prolific. In California tends to bear in alternate years.
Sold as Sharon Fruit after astringency has been chemically removed. Medium-sized, oblate fruits. Ripens in October.
Medium-large oblate fruit, faintly four-sided. Skin deep orange. Flesh light orange, sweet and mild. Ripens late. Keeps well and is an excellent packer and shipper. Tree vigorous, spreading, productive. Most popular nonastringent cultivar in Japan.
Large, roundish-oblate fruit. Skin reddish orange, attractive. When fully ripe has one of the deepest red colors of any persimmon. Flesh quality good, sweeter than Fuyu. Ripens in late October. Tree somewhat dwarf. Bears regularly but sets a light crop in some seasons and is prone to premature shedding of fruit.
Similar to Jiro. Reddish brown skin. Occasional male flowers and seeds. Probably a bud mutation of Jiro. Ripens late October and early November
Medium-sized fruit. Skin burnt orange. Flesh soft, with a good amount of syrup, of fine texture. Flavor very good. Not reliably nonastringent. Ripens early, from the end of September to mid-October. Tree somewhat dwarf. Bears only female flowers. Sets good crop.
Fruit large. Resembles Fuyu, but more truncated and squarish in cross-section. Skin orange-red. Flavor and quality excellent. Ripens late October and early November, ships well. Often sold as Fuyu. Tree slightly upright. Most popular nonastringent variety in California.
Medium-sized, rounded fruit, smoother and less indented than Jiro. Rich orange in color. Sweet and of good quality. Ripens in mid-season. Tree slightly upright. Must be planted with a suitable pollinator to ensure good fruit yield.
Medium-sized, round fruit. Skin orange to deep red. Flesh sweet, of good texture, flavor good. Not reliably nonastringent. Ripens in early November. Tree medium-sized, vigorous, spreading. Differentiates male flowers, making it a suitable pollinator.
Large fruit. Skin orange-red. Flesh dense, very sweet, excellent quality. Difficult to soften on tree (fruit becomes spongy rather than soft). Ripens in November, keeps well Tree almost free from alternate bearing. Recommended for warmer climates.
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