We present the results of millimetre-wave spectroscopic observations and spectral surveys of the following short-period comets: 21P/Giacobini-Zinner in September 2018, 41P/Tuttle-Giacobini-Kresák in April 2017, and 64P/Swift-Gehrels and 38P/Stephan-Oterma in December 2018, carried out with the Institut de RadioAstronomie Millimétrique (IRAM) 30-m radio telescope at wavelengths between 1 and 3 mm. Comet 21P was also observed in November 1998 with the IRAM 30-m, James Clerk Maxwell Telescope, and the Caltech submillimeter Observatory radio telescopes at wavelengths from 0.8 to 3 mm. The abundances of the following molecules have been determined in those comets: HCN, CH3OH, CS, H2CO, CH3CN, and H2S in comet 21P; HCN and CH3OH in 41P; HCN, CH3OH, and CS in 64P; and CH3OH in 38P. The last three comets, classified as carbon-chain typical from visible spectro-photometry, are relatively rich in methanol (3.5–5% relative to water). On the other hand, comet 21P, classified as carbon-chain depleted, shows abundances relative to water which are low for methanol (1.7%), very low for H2S (0.1%), and also relatively low for H2CO (0.16%) and CO (<2.5%). Observations of comet 21P do not show any change in activity and composition between the 1998 and 2018 perihelions. Sensitive upper limits on the abundances of other molecules such as CO, HNCO, HNC, or SO are also reported for these comets.