The level of solar modulation at different times (related to the solar activity) is a central question of solar and galactic cosmic-ray physics. In the first paper of this series, we have established a correspondence between the uncertainties on ground-based detectors count rates and the parameter $phi$ (modulation level in the force-field approximation) reconstructed from these count rates. In this second paper, we detail a procedure to obtain a reference $phi$ time series from neutron monitor data. We show that we can have an unbiased and accurate $phi$ reconstruction ($Deltaphi/phisimeq 10%$). We also discuss the potential of Bonner spheres spectrometers and muon detectors to provide $phi$ time series. Two by-products of this calculation are updated $phi$ values for the cosmic-ray database and a web interface to retrieve and plot $phi$ from the 50s to today (url{http://lpsc.in2p3.fr/crdb}).
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