After you have received the Eon Ticket through event or StreetPass, you can speak to Norman in the Petalburg City Gym. He will explain the ticket and take you to the ferry to go to Southern Island. When there, you will find Latias in Omega Ruby or Latios in Alpha Sapphire, opposite one to the one you were given earlier in the game. After capture, you will find the Soul Dew on the ground.
So if not for that, there's no other way, except for trading, sorry.
In Pokémon Omega Ruby & Alpha Sapphire, the Eon Ticket returned. This ticket is obtained through a variety of methods. The initial download comes from various places such as Play! Pokémon events or stores, or sometimes even special players, but then sends itself through StreetPass to other players, meaning you can get it just by passing any player with the games and the Eon Ticket.
It was given away at:
-Japan: Serial Code in CoroCoro
-North America: Serial Code to Play! Pokémon event organisers
-United Kingdom: Special Eon Ticket Relay event winners then spread it to GAME stores and then on from there
This was way back in 2014, so the only to obtain one now is StreetPassing someone who has the Eon Ticket.