There are many of these. There are even older manuals which have next to nothing. Just try to find an emergency procedure in a 1965 Mooney M20C manual. Does that mean you just die when the DPE pulls the power on you? Or get to say, "well the manual doesn't contain a procedure so you can't test me on it!"?
In the case of the short field tasks, if you want something more modern, there's no short field checklist in the checklists for the Diamond DA40, not even the latest revision of the Jet A diesel FA40NG. As
@MauleSkinner said, the answer is in the performance tables. In the case of other tasks with no POH reference, it's the reason for those
References at the beginning of each task (including the Airplane Flying Handbook). When you don't have a POH way, you use the AFH way.
But you have me curious - the oldest Cherokee manuals I've seen (1964 Cherokee 140 revised in 1973) do talk about short field landing procedures (it's actually the same in their newer models). What do you have?