I can't be sure that this option will work for you, because I don't have more information about your context. Depending on your audience, it may be best to leave it as "Birján".

However, if you would like to translate it to a figure of luck recognised in English-speaking countries and often called on by gamblers, "Lady Luck" could work.

Birján:
"No es claro cual es el origen mitológico de Birján, dios que según algunos, es quien regula la suerte en los juegos de azar. "
http://impreso.milenio.com/node/8939056

Lady Luck:
"When it comes to gambling, most people would like to put their faith in "Lady Luck." It makes sense. Gambling is a game of chance, so winning must be based on how lucky you are.

So, they wait for "Lady Luck," the goddess of fate and chance, to smile upon them. "
http://www.associatedcontent.com/article/26757/the_truth_abo...