Buying BTC with PayPal, preferably automatic, mid 2015
I don't know of any services, especially automatic, which accept PayPal. LocalBitcoins will rarely have vendors accepting PayPal, and even then, it's going to be very much a reputation based judgement call. A vendor accepting PayPal has everything to lose (the Bitcoins and the PayPal money), so I'd be highly doubtful any service would even accept PayPal, let alone without identification or oversight. (Which begs the question, if you want privacy why are you using PayPal?)

Maybe try Bitcoin-OTC or BTCJam if you don't like LocalBitcoins