We present the results of a Herschel survey of 21 late-type stars that host planets discovered by the radial velocity technique. The aims were to discover new discs in these systems and to search for any correlation between planet presence and disc properties. In addition to the known disc around GJ 581, we report the discovery of two new discs, in the GJ 433 and GJ 649 systems. Our sample therefore yields a disc detection rate of 14 per cent, higher than the detection rate of 1.2 per cent among our control sample of DEBRIS M-type stars with 98 per cent confidence. Further analysis however shows that the disc sensitivity in the control sample is about a factor of two lower in fractional luminosity than for our survey, lowering the significance of any correlation between planet presence and disc brightness below 98 per cent. In terms of their specific architectures, the disc around GJ 433 lies at a radius somewhere between 1 and 30 au. The disc around GJ 649 lies somewhere between 6 and 30 au, but is marginally resolved and appears more consistent with an edge-on inclination. In both cases the discs probably lie well beyond where the known planets reside (0.06–1.1 au), but the lack of radial velocity sensitivity at larger separations allows for unseen Saturn–mass planets to orbit out to ~5 au, and more massive planets beyond 5 au. The layout of these M-type systems appears similar to Sun-like star + disc systems with low-mass planets.