Longan, Annonas, Canistel, Jujube, Jabotacaba, Muscadine Grapes, and many many more!
Based on lawace's requirements, Jaboticaba is out of the question. First, it is not sweet; and second, since it is not fast growing, unless he is willing to invest big bucks in a mature tree, it would be not an option (plus, as I said, it is not sweet...sory Adam, I would not base a fruit as sweet if eating a miracle fruit prior to eating the main fruit is a requirement). Jujube may or may not, as while it can have some sweet characteristics, it is also not an outright sweet fruit.
I do agree with Annonas. Longans are not as sweet as a lychee, and some people really do not like the flavor (while easier than a lychee to grow/fruit, the fruit quality from year to year is inconsistent). Canistel, again are a love it or leave it fruit that, depending on the variety can range in quality and sweetness).
Trees I would add to the list are jackfruit, sapodilla, more mango varieties, more lychee varieties, bananas, persimmon, mamey sapote, abiu, purple caimito, carambola, monstera, pineapple, mulberry...the list goes on. A lot depends on one's tastes, wants and of course, how much they want to spend.