A long-term photometric monitoring of a selected sample of solar analogues has been carried out since early nineties as part of "The Sun in tim" project, which is aimed at a multiwavelength study of stars with solar-like global properties, but with different ages and thus at different stages of their evolution. The extended time sequence of ground-based observations collected over more than a decade as part of this program has revealed the existence of starspot cycles. Also from these data it is possible to investigate surface differential rotation of the stars. In this paper we present the photometry collected to date and report on cycles search for a selected subsample of five young single G0-G5V stars with ages between ~130Myr and 700Myr: EK Dra, {pi}^1^ UMa, HN Peg, {kappa}^1^ Cet, BE Cet. Also we include in this study the Pleiades-age (~130Myr) K0V star DX Leo (HD 82443). All the cited stars show activity cycles whose period is, furthermore, the first determined from photometric data. They are compared to those activity cycles derived from CaII H&K emission fluxes and differences are discussed. All the cycle periods, except for EK Dra, fit well the empirical relations with global stellar parameters derived from larger stellar samples. The following results are also inferred from the present study: i) the fastest rotating stars tend to have longer cycles; ii) the range in the observed cycle lengths seems to converge with stellar age from a maximum dispersion around the Pleiades' age towards the solar cycle value at the Sun's age; iii) the overall short- and long-term photometric variability increases with inverse Rossby number with very high correlation degree, indicating that the level of magnetic activity at least in photosphere is still controlled by the stellar rotation even on the longest time scales; iiii) the increase with inverse Rossby number of the long-term overall photometric variability seems to level off at the highest rotation rate, which may be interpreted as due to a saturation in the level of photospheric magnetic activity around the activity maximum.