Its possible to make your own temporary rig, or set up as a live photographer booth. Check out a DIY booth online, its possible.. You will still need a backdrop, and hire someone to do the pictures, it will be time consuming and take up like 3-4 hours of the night.
I did some of that while I was in college. I never used a booth but worked as a roving photographer. For one high school they had a popular place at the prom for photos and we used that. For one at Hadassah we used one of their displays that they had provided. They had the Lord Mayor of Dublin there and everyone wanted their picture taken with him. My friend & I were worried about running out of film. We only had enough for 480 Picture & flash bulbs for the same. We used flash bulbs back in '58 for a lot more than now. I got a strobe a year later.
Photo booths are complicated setups, or at least involved. You need knowledge of manual flash so you can set the exposure to be consistent no matter what's in front of the camera. You need to shoot at least f/8, especially if this will be an unmanned booth with a wireless trigger, to make sure everything is in focus. It helps to have a bench or some place where you know the subject is likely to be and focus around that. If you're controlling the booth, you can focus every shot. If you want an automated booth, you need a wireless trigger. Most people use a PocketWizard with a sync cable to the camera. The booth participants pick up the trigger, click it, and the system fires, hence the involved setup. You have to make it easy for the clients.
Then there's the issue of whether you want the images to display or just save. To display them is a whole other game. You need tethered shooting to a laptop and if desired a large screen or projector, and you essentially need Lightroom to process and display the images as they come in. I suppose you could run a cable from the camera to a TV in a pinch. The backdrop is important only if you care about the background. Plain is the easiest. The subjects are usually more interested in their expressions than the background, so if it's something plain they won't care. This is just stuff to think about.