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 to b) measurement, we observed an increase in the metamagnetic transition field with increasing P-parallel to b. In the c-axis uniaxial pressure (P-parallel to c) measurement, on the other hand, we observed a ferromagnetic transition in zero magnetic field along the c-axis above P-parallel to c = 0.08 GPa. The anomaly of the nuclear spin-lattice relaxation rate divided by the temperature [(T1T)(-1)] at T = 20K is suppressed by P-parallel to b and slightly enhanced by P-parallel to c. The anisotropic uniaxial pressure response indicates that uniaxial pressure is a good parameter for tuning the Ising magnetism in UCoAl.