A new semi-empirical π-electron local coupled cluster theory has been developed to calculate static dipole polarisabilities and hyperpolarisabilities of extended π-conjugated systems. The key idea of the approach is the use of the ethylene molecular orbitals as the orbital basis set for π-conjugated compounds (the method is termed the Covalent Unbonded Molecules of Ethylene method, cue). Test calculations of some small model organic conjugated compounds demonstrate high accuracy of the version of the cue local coupled cluster theory developed in this work in comparison with the π-electron full configuration interaction (FCI) method. Calculations of different conjugated carbon-based oligomer chains (polyenes, polyynes, polyacenes, polybenzocyclobutadiene, etc.) demonstrate fast convergence (per π-electron) of the polarisability and hyperpolarisability values in the calculations when more classes of orbital excitations are included in the coupled cluster single and double (CCSD) excitation operator. The results show qualitatively correct dependence on the system size.