Lambic fruit beers, which are brewed with whole fruit and fermented with wild yeasts that float around in the air, are incredibly sweet and also quite delicious. My favorite is frambois lambic, the raspberry nectar of the gods, but they also come in peach, cherry, black current and apple. They are quite expensive, however- running like 9 buck for 750ml.
UFO makes a pretty good raspberry heffeweisen, Newport Storm makes a blueberry beer. Seasonally Blue Moon does a pumpkin beer. Magic Hat's circus boy is a very pleasantly sweet heffeweisen and they make this new stuff called Miller Chill which has "a hint of lime and salt" which is very lite and sweet but has a kind of lame wine-coolery thing going on.
You could try some good hard ciders- Strongbow is the best and is dry so it probably wouldn't cause heart burn. Woodchuck ciders are super sweet. The Pear is nice, the Amber is better (darker and drier). Again, they border a bit on the wine cooler side of things, but are a little bit tougher. Also try Mead, which is fermented honey and is really tasty