Hi Angela,
There's nothing wrong with asking this question here.
Did you find a suitable solution?
It's hard to advise without knowing what kind of door your closet has. Is it a bifold? Does it have a regular door knob? If it's a regular doorknob, will your landlord allow you to switch it out for a knob with a lock?
I would search Amazon and see what childproof door locks they list. I found some here
Door Locks for Baby. I like Amazon because it's a fast way for me to get customer reviews on products I'm considering. See if you can find the same thing locally if you don't want to go through them. Keep in mind that some of those plastic locks aren't as secure as they may appear.
If you don't need access to the closet while the kids are visiting, can you move a larger piece of furniture in front of the door? If they are frequent visitors then certainly this isn't going to be long term solution.
You might also ask in one of the Parenting sites here at BellaOnline for other ideas.
Good luck!