I also found this site that sends bounce balls through the mail. Bounce Greetings balls are sent fully inflated without any external packaging. They sell for $10, which might get a bit expensive if you have a lot of guests. What a great concept though!
Apparantly, you can send all sorts of things through the mail without external packaging- flipflops, pool noodles, anything that won't break in transit.
If you are really creative, you could do this yourself. Buy an inflated ball at Walmart or Target, grab a marker, handwrite an invitation, some great birthday stamps, and you've got yourself a great greeting card. Come to think about it, these would be great for any other time you just want to cheer someone up.