We present the results of a new multi-site campaign (COYOTES II) to monitor the light variations of T Tauri stars (TTS) of the Taurus-Auriga dark cloud. The UBVRI light curves of 19 TTS were obtained over a two months period to search for rotational modulation by spots. We report new period detections for IQ Tau (6.25d), LkCa-3 (7.2d), and LkCa-14 (3.35d) and confirm previously detected periods for DF Tau (9.8d), DR Tau (9.0d), GM Aur (11.9d), and TAP 26 (2.58d). We also report tentative periods for CW Tau (8.2d), CY Tau (7.9d), HP Tau (5.9d), and XZ Tau (2.6d). No periods were found in the present data set for CI Tau, DG Tau, DQ Tau, GH Tau, RY Tau, Hubble 4, TAP 45, and TAP 57NW. Altogether, the results of this new campaign confirm the main conclusion of COYOTES I that classical T Tauri stars (CTTS) on average have longer rotational periods than weak-line TTS (WTTS). The present study also confirms that rotational modulation in WTTS is due to spots cooler than the photosphere and we show that the amplitude of the modulation primarily reflects the amount of areal coverage by spots. The amplitude of the light variations, and hence the spot size, is found to increase with both rotation rate and advancing spectral type, as expected if WTTS cool spots correspond to photospheric regions of strong dynamo-generated magnetic fields. Finally, combined with previous studies, these new results provide further evidence for temporal variations of the photometric periods of CTTS. Such variations seem to occur preferentially in CTTS whose rotational modulation is dominated by hot spots and we therefore argue that the observed period changes are linked to the magnetospheric accretion process rather than to surface differential rotation.