  Recent investigations into MoB$_{2}$ have unveiled a direct connection
between a pressure-induced structural transition to a P6/mmm space group
structure and the emergence of superconductivity, producing critical
temperatures up to 32 K at 100 GPa. This pressure-induced superconducting state
underscores the potential of doped MoB$_{2}$ as a possible candidate for
metastable superconductivity at ambient pressure. In this work, we demonstrate
that doping by Zr, Hf, or Ta stabilizes the P6/mmm structure at ambient
pressure and results in the realization of a superconducting state with
critical temperatures ranging from 2.4 up to 8.5 K depending on the specific
doping. We estimate the electron-phonon coupling $\lambda$ and the density of
states based on resistivity and specific heat data, finding that $\lambda$
ranges from 0.4 - 0.6 for these compounds. Finally, to investigate the role of
possible metastable defect structures on the critical temperature, we analyze
MoB$_{2}$, MoB$_{2.5}$, and Nb/Zr-doped MoB$_{2}$ using rapid cooling
techniques. Notably, splat-quenching produces samples with higher critical
temperatures and even retains superconductivity in MoB$_{2}$ at ambient
pressure, achieving a critical temperature of 4.5 K.
