There is no way to increase the odds of encountering Pokerus.
Pokérus has a 3 in 65,536 or approximately a 1 in 21,845 chance of being generated on one of the player's Pokémon after a battle, making it rarer than encountering or hatching a Shiny Pokémon.
These are the odds of encountering Pokerus on your own. However, by trading for a Pokémon with Pokerus, you can readily give the infection to your own Pokémon with relative ease. This method is much more convenient for acquiring the infection.
Source: Bulbapedia and GameFAQs