I love teas but have had to refrain from black teas because of my increasing caffeine-sensitivity. Mainly I get gastric irritation, against which there are some tips here.
1) Go for low-caffeine or no-caffeine teas: genmaicha, kukicha, houjicha; and teas not made from the camellia sinensus plant: mugicha, Chinese chrysanthemum tea or herbal teas. Korean grain teas are also not made from camellia sinensus. I used to love black tea chai, but have since switched to YogiTea’s Classic India Spice – same fragrant spices, no black tea.
2) Use the cold-brewing method.
3) Discard the first brew (about 30secs). Subsequent brews are significantly lower in caffeine as it would have leeched out in the first brew. However, only fine teas maintain their taste after repeated brewing, and most of the beneficial antioxidants of green teas would have been lost in the first brewing. See also instructions at Steepology tea blog.
Actually, the subject of caffeine in green tea is a complex one; it depends also on the type of leaf and how it is prepared, among other things. There’s a lot of conflicting information out there, so perhaps the best thing to do is really try and just see how your own body reacts to different teas brewed in various ways.