Rotational properties of late-type low-mass members of associations of known age provide a fundamental source of information on stellar internal structure and its evolution. We aim at determining the rotational and magnetic-related activity properties of stars at different stages of evolution. We focus our attention primarily on members of young stellar associations of known ages. Specifically, we extend our previous analysis in Paper I (Messina et al., 2010, Cat. J/A+A/520/A15) to 3 additional young stellar associations beyond 100pc and with ages in the range 6-40Myr: {epsilon} Chamaeleontis (~6Myr), Octans (~20Myr), and Argus (~40Myr). Additional rotational data of {eta} Chamaeleontis and IC 2391 clusters are also considered. Rotational periods were determined by applying the Lomb-Scargle periodogram technique to photometric time-series data obtained by the All Sky Automated Survey (ASAS) and the Wide Angle Search for Planets (SuperWASP) archives. The magnetic activity level was derived from the amplitude of the V light curves.