The Southern Photometric Local Universe Survey (S-PLUS) is an ongoing survey of $sim$9300 deg$^2$ in the southern sky in a 12-band photometric system. This paper presents the second data release (DR2) of S-PLUS, consisting of 514 tiles covering an area of 950 deg$^2$. The data has been fully calibrated using a new photometric calibration technique suitable for the new generation of wide-field multi-filter surveys. This technique consists of a $chi^2$ minimisation to fit synthetic stellar templates to already calibrated data from other surveys, eliminating the need for standard stars and reducing the survey duration by $sim$15%. We compare the template-predicted and S-PLUS instrumental magnitudes to derive the photometric zero-points (ZPs). We show that these ZPs can be further refined by fitting the stellar templates to the 12 S-PLUS magnitudes, which better constrain the models by adding the narrow-band information. We use the STRIPE82 region to estimate ZP errors, which are $lesssim10$ mmags for filters J0410, J0430, $g$, J0515, $r$, J0660, $i$, J0861 and $z$; $lesssim 15$ mmags for filter J0378; and $lesssim 25$ mmags for filters $u$ and J0395. We describe the complete data flow of the S-PLUS/DR2 from observations to the final catalogues and present a brief characterisation of the data. We show that, for a minimum signal-to-noise threshold of 3, the photometric depths of the DR2 range from 19.9 mag to 21.3 mag (measured in Petrosian apertures), depending on the filter. The S-PLUS DR2 can be accessed from the website: https://splus.cloud}{https://splus.cloud.
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