Using the Parkes Radio Telescope, we have carried out deep observations of 11 unassociated gamma-ray sources. Periodicity searches of these data have discovered two millisecond pulsars, PSR J1103−5403 (1FGL J1103.9−5355) and PSR J2241−5236 (1FGL J2241.9−5236), and a long-period pulsar, PSR J1604−44 (1FGL J1604.7−4443). In addition, we searched for but did not detect any radio pulsations from six gamma-ray pulsars discovered by the Fermi satellite to a level of ∼0.04 mJy (for pulsars with a 10 per cent duty cycle). The timing of the millisecond pulsar PSR J1103−5403 has shown that its position is 9 arcmin from the centroid of the gamma-ray source. Since these observations were carried out, independent evidence has shown that 1FGL J1103.9−5355 is associated with the flat spectrum radio source PKS 1101−536. It appears certain that the pulsar is not associated with the gamma-ray source, despite the seemingly low probability of a chance detection of a radio millisecond pulsar. We consider that PSR J1604−44 is a chance discovery of a weak, long-period pulsar and is unlikely to be associated with 1FGL J1604.7−4443. PSR J2241−5236 has a spin period of 2.2 ms and orbits a very low mass companion with a 3.5-h orbital period. The relatively high flux density and low dispersion measure of PSR J2241−5236 make it an excellent candidate for high precision timing experiments. The gamma rays of 1FGL J2241.9−5236 have a spectrum that is well modelled by a power law with an exponential cut-off, and phase binning with the radio ephemeris results in a multipeaked gamma-ray pulse profile. Observations with Chandra have identified a coincident X-ray source within 0.1 arcsec of the position of the pulsar obtained by radio timing.