Very small asteroids (VSAs) are thought to be the building blocks of larger asteroids and, as such, are interesting to study. Many of these monolithic or deeply fractured objects display rapid rotations with periods as short as several minutes. Observations of such asteroids can reveal their spin limits, which can be related to the tensile strength of their interiors. The evolution of the spins of these objects is primarily shaped by the YORP effect, the theory of which needs comparison with observations. With the 10m SALT telescope, we observed VSAs belonging to near-Earth asteroids. The obtained lightcurves were used to derive synodical periods of rotation, amplitudes, and elongations of these bodies. Results for 14 rapidly rotating asteroids were reported in the first paper in this series. Here we show lightcurves of 2 fast rotators, 9 objects with periods >=1h, and a possible non-principal axis rotator. We also list negative detections that most probably indicate asteroids with long periods and/or low amplitudes. Combining our results with the data from the literature, we obtain a set of 79 near-Earth VSAs with a median period of 0.25h (15min). By adjusting the spin limits predicted by theory to those observations, we find tentative evidence that the tensile strengths of VSAs, after scaling them to the same size, are of the same order as the minimum tensile strengths of stony meteoroids that undergo fragmentation under the atmospheric load.