  We have performed nuclear quadrupole resonance and nuclear magnetic resonance
measurements on UCoAl with strong Ising-type anisotropy under $b$- and $c$-axes
uniaxial pressure. In the $b$-axis uniaxial pressure ($P_{\parallel b}$)
measurement, we observed an increase in the metamagnetic transition field with
increasing $P_{\parallel b}$. In the $c$-axis uniaxial pressure ($P_{\parallel
c}$) measurement, on the other hand, we observed a ferromagnetic transition in
zero magnetic field along the $c$-axis above $P_{\parallel c}$ = 0.08 GPa. The
anomaly of the nuclear spin-lattice relaxation rate divided by the temperature
$\left[ (T_1 T)^{-1} \right]$ at $T$ = 20 K is suppressed by $P_{\parallel b}$
and slightly enhanced by $P_{\parallel c}$. The anisotropic uniaxial pressure
response indicates that uniaxial pressure is a good parameter for tuning the
Ising magnetism in UCoAl.
