You need to add some hysteresis, so that when the green LED lights up it stays on until the charging current rises to a higher value.
simulate this circuit – Schematic created using CircuitLab
When charging current falls to 100mA op amp OA1's output starts to go high and lights D2. Green LED current flows through R3, causing the voltage at OA1's noninverting input to increase from 100mV to ~250mV. This positive feedback 'snaps' the output high and causes D2 to stay lit until charging current rises above ~250mA.
You can change the charging current required to light the red LED by adjusting the value of R3. Theoretically you should also change R2 to make R2 + R3 = 100Ω (which is why I changed R2 to 99Ω), but using a fixed value of 100Ω should be close enough.