Magnetically ordering media support spin waves or magnons, which can couple with electromagnetic waves to form magnon polaritons. Based on insulating antiferromagnets, magnon polaritons are situated in the far-infrared or THz frequency range. We investigated Dyakonov surface magnon polaritons (DSMPs) at the antiferromagnetic surface in an external magnetic field, where the external field and antiferromagnetic easy axis lie in the surface plane and are normal to each other. Our numerical results are based on the MnF2 crystal, but the conclusions and qualitative results are also available to other insulating antiferromagnets. We predicted two field-tunable DSMPs and one tunable Dyakonov surface magnon. We discerned the main effects of the external magnetic field on the DSMPs; either DSMPs are sensitively modulated by the external field or there is a cutoff magnetic field. Their individual Poynting vector seriously deviates the propagation direction and is sensitively controlled by the external field. The spin angular momentum contains two components normal to each other, unlike conventional surface magnon polaritons. One of the DSMPs can carry a huge Poynting vector and spin angular momentum in the external magnetic field. These results are interesting for micromechanics and spintronics and relevant technologies in the far-infrared or THz domain.