Are you brewing your own green tea? If so, be sure that the water is NOT boiling (if it hits the boiling point, let it cool a bit before adding the tea bag to it), and only steep for less than 3 minutes (I've seen recommendations for anywhere from 2 to 4 minutes, but 3 seems about right). If the water temp is too high, or the tea steeps too long, it tends to get bitter. I can't stand the green tea a friend of mine makes, because she uses too-hot water and may steep for too long.
Try sweetening with stevia (perhaps a flavored liquid stevia), or making a pitcher and adding agave nectar and sliced whole organic lemon. Mixes like Tazo Zen (which you can get ready made or in bags) are also a good choice. I also like Inko's ready-made Hint of Mint, with mint (spearmint, I think) and ginger, and no sweetener.
As Beavs said, white tea is good as well (red tea, or rooibos, is not really a tea, as it comes from a different plant, but it is also good).
Another option, as healthy as green tea, and perhaps more, is Yerba Maté. It tastes similar to black tea.
