Hi,
I don't believe tri-state menu items are typically done. For instance, the WPF MenuItem doesn't support it. The reason is that when a menu item is clicked, it closes the menu. So users expect more of a toggle metaphor in that scenario, rather than a cycling between three options sort of metaphor. I think that a tri-state menu item would be confusing for the user.
Instead, I would recommend that you have a popup child menu with three options and put a checkbox next to the currently selected option. That is more traditional UI.