Equation for a capacitor charged by a decaying current source (solar cell)?
As a first approximation, model the solar cell with a Thevenin equivalent circuit as determined by the open circuit voltage, \$V_{OC}\$, and short circuit current, \$I_{SC}\$, of the cell at a given illumination.

Then, for that fixed illumination, the time constant will be:

$$\tau = \dfrac{V_{OC}}{I_{SC}}C $$

The time required to charge to some fraction \$\chi\$ of the final voltage is:

$$t = -\tau \ln(1 - \chi)$$