If you declare it as a "low powered sporting air rifle" it is on the permitted list. The definition doesn't exclude PCP's but my advice to anyone sending me a PCP with a gauge fitted is to send it empty. Pressure vessels and gas cartridges are excluded but if a bottle is screwed on to an air rifle it is classified as part of the air rifle. If bottles are to be sent separate then they should have valves removed and be declared as a flask or tube.
RFD's can send to other RFD's for FAC guns, private individuals can send to private individual or RFD only if it is a sub12 (sub6 for pistols).
If you don't declare the contents of the package it will certainly be x-rayed and sent for destruction if found to be a gun of any description, so declaring as sporting goods is not a good idea. If it has been declared as a "low powered sporting air rifle" and is damaged or lost in transit then you are able to claim but only to the minimum level of insurance (the standard shipping fee for the weight/size) which presently is only £100 so pack your gun well and declare it properly or you may not get any compensation at all if lost or damaged.
In all my years of shipping FAC guns to/from other RFD's and repaired guns back to private individuals I have had no losses or damage caused by PF48. The only gun which I have ever received in a damaged condition was posted to me by a customer who used "MyHermes" against my advice. They refused to pay any compensation saying the gun had been improperly packed and also was on their "banned goods" list so even if properly packed they would not have paid any compensation. After repair the gun was returned via PF48 with no problems.
RMSD will carry air guns but their size limits don't allow rifles, not even take down rifles sadly. Their minimum compensation level is £250 so worth considering if sending an air pistol but be sure to declare it as an air pistol (low powered sporting airgun) and you should be fine.