This is not as easy as it sounds.
Most companies that rent machines support the presentation market and especially conferences and shows. They specialize in delivering and setting up the machines, and they charge a good price for this service.
The prices of machines are now small enough that most people have their own unless they need the special service.
This is like ordering a bottle of champagne at a hotel--they will take good care of you but you pay a lot more than at the discount liquors.
You may pay $200 per day for a machine that now costs under $2000 to purchase outright. But they show up with a truck full of equipment, cables, extra lamps, and make everything work.
I suggest looking up "presentation" "projector" "digital projector" in the yellow pages and calling some of the companies. Your best chance is that you will find a company that has some spare machines when you want them and decide to be nice to you. Drop by and get into a conversation.
But remember this is not their business.