Air rifles over the 500fps are fine to buy in the US and bring over the border. I asked at Customs last year and since then have brought back two. All they asked at Customs was how many FPS it was and which calibre, and asked for my PAL. I showed it to them, they handed it back and that was that. I expected they'd want to see the air rifles but they didn't. They may randomly want to examine them but they didn't for me either time.
In the US, air guns are akin to toys, anyone over a certain age can usually buy them. In Maine they just require you to be over 16. Not sure about shipping but I'd say that if they included a copy of your PAL or your PAL details in the shipping label there would be no more issue than driving it across the border like I have. I got them in the US because they were much less expensive and had many more varieties to choose from.