Delay between input and output.
Naturally.
Digital signal, I assume?
How many bits?
What clock frequency(ies) is(are) available?
Picoseconds? Think nanoseconds. Even very fast logic gates take longer than picoseconds. As a rule of thumb on a typical PCB the speed of a signal is
approx. 15cm/ns or equivalently 0.150 mm/ps or using the inversely 6.7ns/mm. A delay of 1 ps therefore is achieved by a "length" of trace of only 0.15 mm.
There's no use in discussing any logic gates to achieve delay in that order of magnitude. Use a PCB trace of the appropriate length.
Of course, the "exact" delay will depend on details of the layout such as material of the pcb, distance of the trace to other traces or ground planes etc.