Polarimetric studies of pulsars at low radio frequencies provide important observational insights into the pulsar emission mechanism and beam models, and probe the properties of the magneto-ionic interstellar medium (ISM). Aperture arrays are the main form of next-generation low-frequency telescopes, including the Murchison Widefield Array (MWA). These require a distinctly different approach to data processing (e.g. calibration and beamforming) compared to traditional dish antennas. As the second paper of this series, we present a verification of the MWAs pulsar polarimetry capability, using two bright southern pulsars, PSRs J0742-2822 and J1752-2806. Our observations simultaneously cover multiple frequencies (76-313 MHz) and were taken at multiple zenith angles during a single night for each pulsar. We show that the MWA can be reliably calibrated for zenith angles < 45 degree and frequencies < 270 MHz. We present the polarimetric profiles for PSRs J0742-2822 and J1752-2806 at frequencies lower than 300 MHz for the first time, along with an analysis of the linear polarisation degree and pulse profile evolution with frequency. For PSR J0742-2822, the measured degree of linear polarisation shows a rapid decrease at low frequencies, in contrast with the generally expected trend, which can be attributed to depolarisation effects from small-scale, turbulent, magneto-ionic ISM components. This effect has not been widely explored for pulsars in general, and will be further investigated in future work.