The Obama administration plans to announce t0ay that it will make $206 million in bonus Medicaid payments to 15 states — with more than a fourth of the total going to Alabama — for signing up children who are eligible for public health insurance but had previously failed to enroll. The payments, which were established when Congress and President Obama reauthorized the Children’s Health Insurance Program in 2009, are aimed at one of the most persistent frustrations in government healthcare: the inability to enroll an estimated 4.7 million children who would be eligible for subsidized coverage if their families could be found and alerted. Two of every three uninsured children are thought to meet the income criteria for government insurance programs.