In Disgaea 2, there anything I can do to increase the probability of a Mystery Room appearing when I go through the Item World?
Well, as Artless indicated, Mystery Rooms show up every 3 floors.
Can you increase the probability that one shows up on every 3 floors? No. The chance is fixed.
You can, however, "fix" yourself a 100% probability if you have a spare Mr. Gency's Exit. Once you have cleared 3 floors (wherein the first floor had a Mystery Gate), then the next floor is eligible for a Mystery Gate if it isn't a boss floor. If you don't get a Mystery Gate when you first enter that floor, then use the Mr. Gency's Exit to leave the Item World, and save your game. Upon your return to the Item World, the floor will change, and a new chance for a Mystery Gate is rolled. If this also fails, then you reload your save and try again. It usually doesn't take that many tries, the chance isn't particularly low.
If you're trying to maximize an item by getting every Mystery Gate, you're going to need a lot of doors and a lot of patience. So make sure to save up!
Seems to happen after every three floors (clear or skip).
Here's the wiki page for it: