Delaying a TTL signal on the falling edge
I'll have to get going, but really quickly:

This is a digital control problem and should be solved in software. By far easiest, most reliable and accurate. But:

Just as you can use an RC low-pass as delay for both edges, replacing the R with a diode in parallel with an R will make one edge (where the anode side becomes higher than the cathode side of your diode) charge the capacitor very quickly (because the diode then has low effective resistance) whereas the other edge becomes very slow (because then the capacitor has to be discharged through the parallel resistor).







simulate this circuit &ndash; Schematic created using CircuitLab

Typically, for signal cleanliness reasons: 


Buy a diode, a resistor and a capacitor, as well as an IC that integrates two inverters of the desired voltage levels
use first inverter as "buffer"
build "inverse" edge delay circuit as explained above
use second inverter as edge-beautifier