I believe one of two things make it hard for you. I'm not sure which one applies, but I know both have some degree of truth in them
Firstly: For some Pokemon, and legendaries, the chance of them being shiny is calculated when you create the game. It's like a 1 in 8000+ chance, and if it doesn't hit, then no cigar for you unfortunately.
Secondly: If the above doesn't apply for Raikou Entei and possibly Suicune*, then the shiny chance is calculated at the moment they start roaming (I believe. Again I could be wrong; this is coming from what I've read online somewhere).
If the second is true, then it may be possible to influence it before they roam via an AR code, but it still seems unlikely for me.
* Suicune might be different because it's supposed to be a set-up encounter via the storyline, so it's nature/shinyness might be able to be influenced.
But again, I could be wrong, so I'll need a confirmation on this.