We are often ask how to mount items on drywall when you can't align with a stud.
Moen has developed a great wall anchor system, rated at 150 lbs. It can be used to install grab bars in the bathroom, or flat screen TV's (except swing out style mounts). The are available at Lowes and Menards that I know of. They worked great for me to install grab bars in my SIL bathroom.