If you aren't fond of herbal teas in general because the taste is a little too distinctive then I recommend a tea called Rooibus, also known as Redbush. You can find this tea at your local Holland and Barratt (there's even an Earl Grey variety) and I know that Tesco also sell it, I'm not sure about other supermarkets. This tea is caffeine free and very mild and smooth, what's more, you can drink it with milk if that's how you like your tea.
I only ever drink herbal tea so I have a bit of a taste for that sort of thing but I can tell you that I have converted many friends who are hardened tea and coffee drinkers, so I'd recommend you give it a try, it is certainly the most pleasant tasting tea for those who aren't used to the strong flavour of other herbal teas.
Rooibus is also known for its powerful healing properties and has as many antioxident elements as green tea. I believe it would help with your ulcers, it certainly won't make them worse!
This website will tell you a bit more about where it comes from and how good it is for you
http://www.redbushtea.com/home.asp
Enjoy!