You did not mention the load this drives, nor the spacing between pulses ?
You have a 3V swing, so any MCU or logic put between -2V and -5V rails will give that.
Most CMOS Logic / MCUs will be slightly faster rise times than your display.
CMOS logic would need a sprinkling of parts - something like a HC4017 gives you some pulse choices.
Or, almost any small MCU could do that, either use PWM + SW, or just SW alone bit-bang.
A 50MHz Sysclk will have 20ns granularity in timing.