Using first principles calculations, we show that Li_xAl_yB_2(x+y) materials have strong electron-phonon coupling, with many having a superconducting critical temperature (T_c) that exceeds that of the more familiar MgB_2 at ambient pressure. In particular, we find that LiAlB_4 is the most stable member of the family, with T_c>44K whilst the peak T_c is with Li_3AlB_8 which has T_c>77K. Our results reveal that these materials are both thermodynamically and dynamically stable, with strong electron-phonon coupling, indicating significant potential for practical superconducting applications
