Ask Mr. Smarty Plants

There are two native persimmons in North America, Diospyros virginiana (common persommon) and Diospyros texanum (Texas persimmon) and the astringent tannins present are highest in the immature fruit.

From the Lady Bird Johnson Wildlfower Centre Native Plant Database, here is some information about these fruit producing trees...

Diospyros virginiana

In old fields, common persimmon is a low, shrubby tree, 15 ft. tall. In rich, moist soil the species becomes a large tree, up to 100 ft. tall, with a spreading crown and pendulous branches. Bell-shaped, yellow flowers are hidden by half-grown leaves. Large, oval, mature leaves usually become yellow-green in fall. The large, orange, edible fruit attracts wildlife. On old trunks the bark is thick and dark-gray to almost black and broken into scaly, squarish blocks. Common persimmon is deciduous. Best-known by its sweet, orange fruit in autumn.

When ripe, the sweet fruit of Persimmon somewhat recalls the flavor of dates. Immature fruit contains tannin and is strongly astringent. Persimmons are consumed fresh and are used to make puddings, cakes, and beverages. American Indians made persimmon bread and stored the dried fruit like prunes. Opossums, raccoons, skunks, deer, and birds also feed upon the fruit. Principal uses of the wood are for golf-club heads, shuttles for textile weaving, and furniture veneer. The word persimmon is of Algonquian origin, while the genus name Diospyros, from the Greek, means fruit of the god Zeus.

Diospyros texanum

Shrub or small tree with very hard wood, usually multi-trunked. Normally 10-15 ft tall but can reach 35 ft in the southern parts of its range. Common in brushy areas on level uplands, stony hillsides, and lower slopes from Houston and Bryan, Texas, in the east, west to Big Bend in west Texas and south to Nuevo Leon in northeastern Mexico. Very common in central and south Texas. Bark light gray to white, smooth, thin, on some trunks peeling in rectangular flakes and exposing a pinkish layer beneath. Leaves up to 2 inches long, but most about half this length, firm textured, rounded or slightly notched at the tip and tapering to the base; margins smooth, rolled down. Flowers urn shaped, whitish, about 3/8 inch wide, arranged singly or in small clusters among the new leaves; male and female on separate plants, appearing in March and April. Fruit fleshy, round, up to 1 inch in diameter, black and sweet when ripe, ripening from late July into September.

This well-shaped, small tree is valued primarily for its striking trunk and branches, which are a smooth, pale greyish white or whitish grey, peeling off to reveal subtle greys, whites, and pinks beneath. The fruits, borne on female trees, are edible once soft, with a flavor some liken to prunes, and are favorites of many birds and mammals. It is extremely drought-tolerant and disease-resistant and is ideal for small spaces in full sun. The heartwood, found only in very large trunks, is black, while the sapwood is clear yellow.

From wikipedia here is some information about persimmon tannins:

Astringent commercial persimmons contain very high levels of soluble tannins and are unpalatable if eaten before completely softened. However, the sweet, delicate flavor of fully ripened persimmons of varieties that are astringent when unripe, is particularly relished. The astringency of tannins is removed in various ways. Examples include ripening by exposure to light for several days, and wrapping the fruit in paper (probably because this increases the ethylene concentration of the surrounding air). Ethylene ripening can be increased in reliability and evenness, and the process can be greatly accelerated by adding ethylene gas to the atmosphere in which the fruit are stored. For domestic purposes the most convenient and effective process is to store the ripening persimmons in a clean, dry container together with other varieties of fruit that give off particularly large quantities of ethylene while they are ripening; apples and related fruits such as pears are effective, and so are bananas and several others. Other chemicals are used commercially in artificially ripening persimmons or delaying their ripening. Examples include alcohol and carbon dioxide which change tannin into the insoluble form. Such bletting processes sometimes are jumpstarted by exposing the fruit to cold or frost. The resultant cell damage stimulates the release of ethylene, which promotes cellular wall breakdown.

Astringent varieties of persimmons also can be prepared for commercial purposes by drying. Tanenashi fruit will occasionally contain a seed or two, which can be planted and will yield a larger more vertical tree than when merely grafted onto the D. virginiana rootstock most commonly used in the U.S. Such seedling trees may produce fruit that bears more seeds, usually 6 to 8 per fruit, and the fruit itself may vary slightly from the parent tree. Seedlings are said to be more susceptible to root nematodes.

The non-astringent persimmon is squat like a tomato and is most commonly sold as fuyu. Non-astringent persimmons are not actually free of tannins as the term suggests, but rather are far less astringent before ripening, and lose more of their tannic quality sooner. Non-astringent persimmons may be consumed when still very firm, and remain edible when very soft.

There is a third type, less commonly available, the pollination-variant non-astringent persimmons. When fully pollinated, the flesh of these fruit is brown inside and the fruit can be eaten firm. These varieties are highly sought after and can be found at specialty markets or farmers markets only.

Before ripening, persimmons usually have a "chalky" taste or bitter taste.