I don't have an easy answer to share, but there are interesting questions behind it. One, implied by your original question, is the mechanisation of the artificial feel - if it's introduced. I think think of a number of mechanisms that may matter:-
- Manoeuvre stability (good old "stick force per g")
- Pull force to stall
- Stick fixed apparent LSS
- Q-feel: which at the very least should influence the last of the other three.
Civil standards define manoeuvre stability (typically max 15lbf pull to exceed N1). Part 25 variants usually mandate some kind of PFTS minimum (about 10lbf I think?) but the lower civil codes don't. Some research has been done showing that they should. All of this, of course, assumes a contentional stick or yoke.
There's research indicating minimum aLSS gradients for good controllability. For low performance light aircraft, I've found about 0.1daN/kn works about right as a minimum, but higher performance aeroplanes, probably with higher ability pilots - you're likely to be happy with a shallower gradient. None of this is defined in any regulations that I recall however.
I'm not as familiar with it as I used to be, but if I was looking for useful guidance for military stick force gradients, I'd be wading through UK Def-Stan 00-970 part 1. That does contain quite a lot, and you might find some old but still good material in the old UK BCAR Sections K and D.
However, pretty much all of that was written around either reversible control systems, or hydraulic control systems trying to emulate those. For FBW, I suspect that most useful advice sits in company design handbooks, and agreements between those companies and their authorities, and thus will be very difficult to access.
I think perhaps you might find some useful guidance if you wade through some AIAA conference databases. That's where quite a lot of the company research *might* find its way into the public domain. But, clearly, it's not authoritative - it's research that you'd have to negotiate your way into using in a design.
With regard to sidesticks specifically - I've been involved in basically setting up some experimental work and analysis to come up with numbers. I don't have access to that data any more, but as I recall we basically took the standard numbers in CS23 and related documents, showed the geometry that typically applies to - the mapping that to the geometry of the sidestick, particularly considering the geometry of support of the forearm, and how that affected it. Then we took the results to our authority, and negotiated agreement for standards that we'd apply as "equivalent safety" to the more conventional stick or yoke case the design codes are written around.
G