Use capacitor to turn on led when power is off
Maybe something along these lines. When SW1 is closed, C1 charges through D4 + D2 + R3 and D3 (green) is illuminated. R3 limits the current when SW1 is initially closed.
When SW1 is opened, D3 goes dark and D1 (red) is illuminated, and the current through it decreases (more or less) exponentially towards zero.



simulate this circuit &ndash; Schematic created using CircuitLab
In this simulation, the switch is opened at T = 1 second.