In an attempt to stem the rising tide of illegitimacy rates and single-parent families among the poor, which act mandated two-parent coverage for all state afdc programs?

I believe the answer is: Family Support Act

The family support act was created in 1988  which is aimed to Aid to Families with Dependent Children (AFDC) with various programs in the form helps in finding jobs, Child support for the parents who couldn't sustain their children themselves, and family benefits to obtain cheaper programs depending on the number of kids they have.