RC Circuit Analysis - Finding Capacitance
This case is usually slightly more complicated than series RC, but in the end is the same concept, if you want to see the equations developed look for thevenin RC parallel circuit online. Plenty of sources should come up.

your current equation for R2 looks like this

$$
I(R2)=\frac{V}{R1+R2}(1-e^{-\frac{(\frac{R1}{R2}+1)t}{R1C}})
$$

if you multiply this by R2 you get the voltage in R2 by Ohm's law so no worries about that. Or just work directly in current for 4 volts you want 4mA flowing through R2 if it is 1k.

For RC design in general you want to find a Capacitor of the right order and tweak the resistor values, because you have many more values available for resistors so as a general approach I would set a general range for the capacitor like say 1uF, plot with your current resistors and see how long it takes to reach 4mA.

Of course you can always simulate this circuit with LTspice fairly quickly and avoid solving the equation every time, just make the schematic and plot every time changing C values until you find something that suits you if you cannot change R values.