Take her to a fine restaurant. Order tapioca, and hide a beautiful diamond ring in it. When she chokes on the ring, perform the heimlic maneuver on her (being the hero you are). When she recovers, ask her hand in marriage, and place the ring upon her finger.
Well, of course. You said, "convincingly." This method is convincing.
Make the day all about her. Send her on a "treasure hunt" or something. If you're not worried about money, that is. Choose a day when you both have no obligations. If you are living together, leave on the pillow next to her a rose and a note that says something to the effect of, "Baby, today is all about you. Be at the 'such and such salon' at 10am sharp for the surprise of your life! I love you!" Send her to a spa to be pampered, hair, nails, massage, the works. Then, through a note left at the salon, send her shopping for a dress and shoes. Maybe top it off with a meeting at her favorite restaurant or even the place you first met or shared your first kiss where you propose on bended knee. Just an general idea. Make it your own if you'd like to embellish upon it. Make the day romantic. Hope that helps. :) Talk to your female friends/family members, or even HER family and friends. They can help you make the day very special for her.