Congratulations, this is one of music's minefield questions. There is no single answer, and any attempt to give a complete answer will result in a set of books about the size of Encyclopedia Britannica.
Why is this so?
First, "keys" on a harpsichord or organ can mean key as in key signature: it is a temperament/intonation question. Depending on how the instrument is tuned, and whether the desire is for "useful keys", the answer is between 4 and 12, 24 if you consider major and minor separately. (If you had asked the more precise "modes", the number would be larger and perhaps more variable.)
Of course, you are not asking a temperament question, but I threw that in for 'completeness', which is regrettable since, as I have said, completeness is not easy to achieve.
Since you are asking how many keys as in how many bits you can push down to sound a note, we can look more closely at what is meant by "harpsichord" and "Organ". The term "harpsichord" refers to any number of keyboard instruments where the strings are plucked by a mechanism which initiates at a 'key'. This includes portable ottavini (plural of ottavino, 4'-foot, single voice keyboard instrument about that you can carry under one arm) at one end of the spectrum, and extends to massive Flemish harpsichords with two keyboards (or, potentially, three, although I don't remember one of those just offhand.) An ottavino with 3 octaves is not beyond belief (since I've held one in my hands) and the full flemish layout can approach the 88 keys of a piano. Many harpsichords did not have a complete octave at the bass end, though, and had just five or six keys whose strings were tuned to most-used lowest bass notes.
Organs can be even worse: the term applies equally to any member of the family, from the little portatives with an octave of keys to the mighty Wurlitzer theatre organ, with four wrap-around keyboards, full pedalboard, a small keyboard (one to 3 octaves, I believe) for the 'toys' and a 2-octave synthesizer retrofitted. While this may seem artificial, there are pipe organ consoles in historical churches with full tracker action (i.e., no electronics or electro mechanics like the Mighty Wurlitzer) with as many keyboards.
In short, these instruments have between a 900 and 1600 year history (if you count Hero's water organ) and there has never been an established "standard" instrument in either family.
Oh, while you're counting keys to make your massive compendium of harpsichord and organ keyboards, don't forget the hidden mines: the bottom octave or so on the Hammond organs (B3 version is most popular, used a lot in Rock in the 60's on) aren't for playing notes: they select the tone and percussive effects on the keys which make notes! This raises a whole new problem: are these key-shaped things to be counted as keys? If so, are the other oddly-shaped keys which select tonalities (either filters or additive ranks or by adding sets of strings on harpsichords) to be counted? After all, the only real definition of a key is that it is something you 'touch' with your fingers to actuate a mechanism ...