Answer: It sounds as if your tree may not be getting enough light because of the tall canopy of trees. The fact that you did get fruit the first year and they molded before ripening is another indicator that you don't have enough light. Depending on how it's planted, your tree may also be trying to compete with the large trees' roots for nutrients and water. Also, 'Reliance' peaches will never be quite as soft as a southern peach.
It evidently is still a young tree, so it may not be mature enough yet to produce a lot of fruit. Another possibility to having no fruit is that you may lack insect activity during the blooming period. Your tree is self-fruitful, but it still needs pollinators to be active when the tree is in bloom. If your tree had lots of flowers but no fruit, I'd suspect that either the blossoms were killed by a late cold snap or there weren't enough pollinating insects around. When weather is cold or rainy, honey bees are reluctant to fly, and that sometimes spells disaster for fruit tree crops. Encourage pollinators to visit your yard by planting a variety of flowers.
To improve your chances for fruit, make sure the tree gets plenty of water and is fertilized once a year in the spring with composted manure, compost or a general garden fertilizer. If possible, you might consider pruning some of the surrounding trees to let in more light or even moving the peach tree to a sunnier spot.
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