A panini press is really nothing more than heat and weight. As has been previously suggested, you can use what you have on hand to accomplish that end. I've used cast iron, foil-wrapped bricks, etc. and all have been mentioned here. Just use what you can find around your kitchen/home and you'll be fine.
"As a girl I had zero interest in the stove." - Julia Child
This is real inspiration. Look what Julia became!