We have investigated with the pulsed ESR technique at X- and Q-band frequencies the coherence and relaxation of Cu spins S = 1/2 in single crystals of diamagnetically diluted mononuclear [n-Bu₄N]₂[Cu(opba)] (1%) in the host lattice of [n-Bu₄N]₂[Ni(opba)] (99%, opba = o-phenylenebis(oxamato)) and of diamagnetically diluted mononuclear [n-Bu₄N]₂[Cu(opbon-Pr₂)] (1%) in the host lattice of [n-Bu₄N]₂[Ni(opbon-Pr₂)] (99%, opbon-Pr₂ = o-phenylenebis(N(propyl)oxamidato)). For that we have measured the electron spin dephasing time T_m at different temperatures with the two-pulse primary echo and with the special Carr-Purcell-Meiboom-Gill (CPMG) multiple microwave pulse sequence. Application of the CPMG protocol has led to a substantial increase of the spin coherence lifetime in both complexes as compared to the primary echo results. It shows the efficiency of the suppression of the electron spin decoherence channel in the studied complexes arising due to spectral diffusion induced by a random modulation of the hyperfine interaction with the nuclear spins. We argue that this method can be used as a test for the relevance of the spectral diffusion for the electron spin decoherence. Our results have revealed a prominent role of the opba^4- and opbon-Pr₂ ^4- ligands for the dephasing of the Cu spins. The presence of additional ¹⁴N nuclei and protons in [Cu(opbon-Pr₂)]^2- as compared to [Cu(opba)]^2- yields significantly shorter T_m times. Such a detrimental effect of the opbon-Pr₂ ^4- ligands has to be considered when discussing a potential application of the Cu(II)-(bis)oxamato and Cu(II)-(bis)oxamidato complexes as building blocks of more complex molecular structures in prototype spintronic devices. Furthermore, in our work we propose an improved CPMG pulse protocol that enables elimination of unwanted echoes that inevitably appear in the case of inhomogeneously broadened ESR spectra due to the selective excitation of electron spins.