Currently there are two exchanges that offer direct XMR/AEON conversion each with its own limitations/warnings. The third option would be direct OTC trades (optionally with an escrow agent to reduce risk).

Cryptopia offers the most XMR trading pairs of any exchange including an XMR/AEON pair. Its current limitation is very low trading volume compared to the Poloniex (first exchange that offered Monero trading pairs including XMR/AEON previously). Changelly operates in a manner similar to Shapeshift but unlike Shapeshift offers Aeon trading and direct XMR/AEON conversion. It receives a large level of distrust within the Monero community due to its connection with Minergate There is a Bitcointalk thread designed to connect buyers and sellers hoping to arrange OTC trades. IRC trading at ​#monero-otc is another option LocalMonero also provides an OTC platform for XMR/AEON trades.

The centralized exchange with the most Aeon volume is Bittrex. It was not mentioned in my answer above because they do not offer a XMR/AEON trading pair. Bittrex does offer both a BTC/XMR trading pair and a BTC/AEON trading pair.