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