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The aim of this work is to characterize HCN and CH$_3$OH emission from recentcomets.  We used the Onsala 20-m telescope to search for millimetre transitions of HCNtowards a sample of 11 recent and mostly bright comets in the period December2016 to November 2019. Also CH$_3$OH was searched for in two comets. The HCNsample includes the interstellar comet 2I/Borisov. For the short-period comet46P/Wirtanen we could monitor the variation of HCN emission over a time span ofabout one month. We performed radiative transfer modelling for the observedmolecular emission by also including time-dependent effects due to theoutgassing of molecules.  HCN was detected in 6 comets. Two of these are short-period comets and 4 ofthem are long-period. Six methanol transitions were detected in 46P/Wirtanen,enabling us to determine the gas kinetic temperature. From the observations, wedetermined the molecular production rates using time-dependent radiativetransfer modelling. For 5 comets, we could determine that the HCN mixing ratioslie near 0.1% using contemporary water production rates, $Q_\mathrm{H_2O}$,taken from other studies. This HCN mixing ratio was also found typical in ourmonitoring observations of 46P/Wirtanen but here we notice deviations, on adaily time scale, up to 0.2% which could indicate short-time changes in theoutgassing activity. From our radiative transfer modelling of cometary comae,we found that time-dependent effects on the HCN level populations are of theorder 5-15% when $Q_\mathrm{H_2O}$ is around $2\times 10^{28}\,\mathrm{mol\,s^{-1}}$. The effects may be relatively stronger for comets with lower$Q_\mathrm{H_2O}$. The exact details of the time-dependent effects depend onthe amount of neutral and electron collisions, radiative pumping, and molecularparameters such as the spontaneous rate coefficient.

Emission from HCN and CH$_3$OH in comets. Onsala 20-m observations and radiative transfer modelling