I'll chip in some more info for the PT239x based crowd.
Unlike clock based delays the PT239x do not have an external clock input. They have an internal clock whose frequency adjusted by an external resistance. The accuracy of the internal clock is not know as Princeton does not publish that information from what I have seen.
Another issue is the relationship of resistance to time for the clock is not very well known. Even with what information that has been published it results in an odd shaped log-ish curve. The idea of using this IC or another clock source with a linear time to output relationship will not work. Neither will using a optocoupler of some sort as it will never match this odd shape curve.
Digital delays do not suffer from these issues as all the math is done in one common part sharing the same clock source so they can be accurate. With analog and multi-IC digital delays this is not the case so there is room for accuracy problems. One of the questions that needs to be asked is how accurate do you want to be ?
If you need absolute accuracy then you will be hard pressed to develop something or atleast something within a reasonable amount of resources. If you are willing tolerate alittle bit of inaccuracy then you can get something working within reasonable resources.
So after all that can a reasonably accurate simple tap tempo be made for the PT239x ? YES! In fact someone may already have done that.

Andrew