the fact that red wine is fermented with the skin means that there is always going to be tannin in the wine and will generally be 澀或酸. "Rose" would be something u can try or just try something that had aged for over 5 years...
try wine made with Merlot or go with bigbilly2003's suggestion. Wine from Rhone in general is rounder. Also, cheap wine usually is strong on tannin, and it give me headache too. Go with the nicer one (CAD$25 or above), you will able to tell the different.