CoralCDN works a bit differently than Swarm CDN, in that you don’t have to make any changes to your code, no extra scripts or iframes are loaded, and it’s not reliant on your visitors using a particular browser.
I have never run more than one CDN solution on a site before, so I can’t say how the two will work together. I can tell you that the CoralCDN plugin simply rewrites the URL of your images when the page is loaded (not in the database itself) and makes no other lasting changes. Swarm CDN says you’ll need to enable a special function in their settings page if you don’t load your images from your own domain, so you may need to make this change if you’re using any additional CDN (CoralCDN included).
As the Swarm CDN plugin author noted (above), it’s worth trying them both and see which works best for you.