The best FAC air rifle for my money is the Edgun. Its regulator and firing valve are just SO efficient and it is a pretty compact bullpup design. Mine was a .22 running at 40 ft lb and delivering 40 shots with a 200BAR fill to a fairly compact air tube. I sold it only because as a left handed shooter, the magazines stuck in my face. The Rapid and Air Ranger are also excellent rifles at FAC power levels but are inevitably larger and heavier than the bullpup Edgun.
I agree with the post above regarding the FN19-it is reasonably light and certainly very cheap to buy. Also very reliable and easy to work on.
If weight is an issue-it usually is- I have made a lightweight Rapid which weighs in at around the 3 KG level with scope. That is about the same as a Falcon Lighthunter with skeleton stock. Mine is a regulated .20 with a short barrel, high spec firing valve and skeleton stock. With a 280cc bottle I get around 3 magazines (36 shots) regulated at nearly 900 ft sec (25 ft lb with the JSB Heavy pellets) in .20. This is a very effective, light, compact and powerful air rifle and is my go-to gun most of the time.
'It may be that your sole purpose in life is to serve as a warning to others'.