I don't see any reason a switch debouncer wouldn't work. For example, in the circuit I posted, pulling Pin1 of the switch low (i.e., the high-low transition in what you drew) creates a single pulse of width defined by the 555. It cannot be retriggered until the switch is re-opened (i.e., the high in your signal). Other latch debouncers act similarly.
It is true you get a pulse on LOW, rather than HIGH, but that is a simple thing to invert.
Is the signal you are counting regular? That is, are the high and low times regular are does one or both vary? In the 555 debouncer, for example, the low times can be whatever you want them to be, but the high pulse is fixed (before inversion). The flip-flop debouncers don't have that restriction.
John