Can you explain what your circuit is supposed to do? In simulation it doesn't seem to do anything.
This will do pretty much what you require.
C1 is the filter capacitor of your unregulated supply.
D1, 2, 3 serve to create a voltage drop while current is flowing that will allow a red LED (D4) to light during charging.
U1 is an LM317 with R1 determining the max current. This should be set to the lesser of the ripple current for your capacitor and the max current from your power supply.
U2 is another LM317 with R2/R3 determining the output voltage (it should be set to 2.2V.
Ignoring esoteria like switchmode regulators, this will charge your capacitor to 2.2V as quickly and safely as is possible given your capacitor and power supply.
If charge time is less of a consideration, removing U1 and R1 and replacing them with a simple resistor would also be OK.
In this configuration your input voltage needs to be at least 6 volts higher than your capacitor voltage.