  Excitation, detection and control of coherent THz magnetic excitation in
antiferromagnets are challenging problems that can be addressed using ever
shorter laser pulses. We study experimentally excitation of magnetic dynamics
at THz frequencies in an antiferromagnetic insulator CoF$_2$ by sub-10 fs laser
pulses. Time-resolved pump-probe polarimetric measurements at different
temperatures and probe polarizations reveal laser-induced transient circular
birefringence oscillating at the frequency of 7.45 THz and present below the
N\'eel temperature. The THz oscillations of circular birefringence are ascribed
to oscillations of the magnetic moments of Co$^{2+}$ ions induced by the
laser-driven coherent E$_g$ phonon mode via the THz analogue of the transverse
piezomagnetic effect. It is also shown that the same pulse launches coherent
oscillations of the magnetic linear birefringence at the frequency of 3.4 THz
corresponding to the two-magnon mode. Analysis of the probe polarization
dependence of the transient magnetic linear birefringence at the frequency of
the two-magnon mode enables identifying its symmetry.
