Two short pulses generated when input goes high

Solution 1:

You can use a classical piston short pulser and multiply the output. Here's a schematic depiction (top and side view).

Place a sticky piston with a block on top (yellow), and place a repeater facing into the block. This is your input (green). Place redstone dust on two sides of the block. Powering the block will cause the piston to extend after 1 tick, but before that, the dust will be powered. Use repeaters to delay one of the signals by at least 2 ticks. Since it's only a one-tick pulse, you have to use multiple 1 tick repeaters, IIRC (2 ticks might work).

The piston will retract when your input signal turns off.