We show that the well-known Kohn anomaly predicts T_c for ordered AlB₂-type structures. We use ab initio density functional theory to calculate phonon dispersions for Mg_1−xAl_xB₂ compositions and identify a phonon anomaly with magnitude that predicts experimental values of T_c for all x. Key features of these anomalies correlate with the electronic structure of Mg_1−xAl_xB₂. This approach predicts T_c for other known AlB₂-type structures as well as new compositions. We predict that Mg_0.5Ba_0.5B₂ will show T_c = 63.6 ± 6.6 K. Other forms of the Mg_1−xBa_xB₂ series will also be superconductors when successfully synthesised. Our calculations predict that the end-member composition, BaB₂, is likely to show a T_c significantly higher than currently achieved by other diborides although an applied pressure ∼16 GPa may be required to stabilise the structure.