Secure private key storage
RFC 5958 and RFC5959
seems to be the latest standard for storing encrypted private keys.
It obsoletes RFC 5208, also known as PKCS#8.
My understanding is that AES is one of the many encryption algorithms supported by RFC 5958.

The GNU Keyring File Format is a another standard for a file format that stores private keys using AES-128.

The Gnome Keyring implementation stores private keys using (among other things) AES-128 encryption.
Alas, it doesn't seem to follow any published standard, but perhaps it can be seen as a de-facto standard.
The Gnome Keyring FAQ briefly mentions that sometime in the future (after 2010) it will transition to "a standard way of encrypting the keyring" (PBKDF2) which apparently requires "A new file format" (perhaps one of the above formats?).