This is key for any character really. You need to give your character their own voice and really develop their personality. What I've always done was visualize myself as my actual character while I'm writing or coming up with my RP. Put yourself in the role rather then just the writer for the character. If you can really dive deep into your character, you'll be able to write more naturally and your dialogue in the piece will improve as well. Visualizing the writing is easily one of the best ways to improve your writing. See it in your head as it unfolds and write down what you're seeing.
True story: when penning the more difficult RPs for Dragon I've been known to pace up and down smoking an imaginary cigarette. I don't normally go in for that kind of method writing (is that even a thing? It is now), but it worked out pretty well here.
When I was starting up as a writer I used to struggle with character voice a lot. Dialogue was pretty much the last thing I learned how to do; everyone ended up sounding like me (good thing I totally got over that problem snarf snarf) instead of like the character I was envisioning. Early on I found the best way to get a character across was to cheat. Instead of writing a situation and then trying to pen my character's reaction to it, I would decide first what personality traits I wanted to get across to the reader and then craft a circumstance specifically tailored to bring those personality traits out.
It's fucking terrible advice in the long term, but it's a quick fix that worked for me.