Greetings and welcome to the site.
You have my permission to include DesktopCoral with your program.
The only thing you need to be aware of is that when you do so, users will not have a license key installed for it, which means that, while the program will continue to run fine, it will show them a message on startup asking them to visit our site for a free license key. That's an important part of how we make sure people know we depend on user donations. As long as you are ok with that (and don't include *your* license key along with the installation), then you certainly have our permission.