Single hadron azimuthal asymmetries in the cross sections of positive and negative hadron production in muon semi-inclusive deep inelastic scattering off longitudinally polarised deuterons are determined using the 2006 COMPASS data and also all deuteron COMPASS data. For each hadron charge, the dependence of the azimuthal asymmetry on the hadron azimuthal angle $ϕ$ is obtained by means of a five-parameter fitting function that besides a $ϕ$-independent term includes four modulations predicted by theory: $\sinϕ$, $\sin 2 ϕ$, $\sin 3ϕ$ and $\cosϕ$. The amplitudes of the five terms have been first extracted for the data integrated over all kinematic variables. In further fits, the $ϕ$-dependence is determined as a function of one of three kinematic variables (Bjorken-$x$, fractional energy of virtual photon taken by the outgoing hadron and hadron transverse momentum), while disregarding the other two. Except the $ϕ$-independent term, all the modulation amplitudes are very small, and no clear kinematic dependence could be observed within experimental uncertainties.