I can't stand coffee, but I have had a similar problem with tea. Somebody recommended that I add ginger to my tea. It seems to have helped. (It has been used to similar effect for morning sickness.)
Ginger tea is well known to sooth digestive issues. I like to make what the Mexicans call Jamaica water or hibiscus flower tea instead of caffeinated tea from the Far East for casual drinking through out the day. It has lots of vitamin C. I add a sweetener such as agave or honey, and a good squeeze of fresh lime juice. Celestial Seasonings sells the tea bags under the name of Red Zinger tea in the US or you just order a bag of the flowers on the internet which is what I do.