Just get a passport. Like it's been mentioned, it easy to get, not that expensive, and you really should have one anyway.
If you go to Niagra Falls, you pretty much have to go to the Canada side to make the trip worthwhile. Casino Niagra is one place I'd recommend.
You are asking for serious trouble/hassle if you don't take a passport or, in the very least, your birth certificate (an orginal one, not a photocopy) and ID with you. Getting into Canada isn't that big of a deal - it's getting back into the U.S. where you encounter all the problems.