First, don't list the monitor on eBay until you have the packing question resolved - you don't want your buyer to have to wait for you to figure this out later.
Second, with so many people selling things on eBay these days, lots of stores now sell packing materials, including styrofoam peanuts and bubble wrap. I'd be surprised if there isn't a store somewhere near you that does packing and shipping, but if there really isn't, how about a Walmart? They might well have some of the supplies you need.
Worst case scenario, you can order the supplies you need on eBay. Plenty of sellers have figured out that there's money to be made in packing supplies - and you'll find lots of listings for them. So, if you really can't find anything available locally, you can go this route (and it may be even cheaper than what you'd find locally).
Where I live, the town dump also has a recycling center - and free peanuts and packing boxes are usually readily available. But I don't know if this is common in other locations.
Good luck!