When teen heartthrob Justin Bieber signed on to promote a prepaid debit card created by BillMyParent, the profile of “tween Cards” got a big boost. Cards and accounts targeting underage consumers and their parents have had a slow start in the market, but with consumers’ increased reliance on electronic payments, more feature-rich and mobile enabled account management tools, a new segment of the underserved market may be poised to make some gains.