How can I include a newline in a constant in C#

There are three issues here. The first is that if you have a lot of text, you shouldn't be including that in the source code directly anyway. For small localizable pieces of text, you can use a resx/resources file - Visual Studio will present you with a grid so you can specify text for a particular resource name etc.

For lots of text, however, I'd strongly consider creating a .txt file which you embed into your assembly, and read with Assembly.GetManifestResourceStream. It's much easier to edit a text file than to manage large blocks of string literals.

The rest of the answer, however, addresses the question you actually asked, about string literals.

Second is getting a line break into the string, which can be done either by including it directly using escape sequences:

await UserManager.SendEmailAsync(2, "Confirm your account", 
    "Please confirm your account by clicking this link:\r\n<a href=\"www.cnn.com\">link</a>");

(Here \r\n is a carriage return and line feed. Sometimes you may want just \r or just \n. It depends on the context.)

Or a verbatim string literal:

await UserManager.SendEmailAsync(2, "Confirm your account", 
    @"Please confirm your account by clicking this link:
      <a href=""www.cnn.com"">link</a>");

Note that in a verbatim string literal, you need to escape double-quotes by doubling them, as a backslash is just a backslash.

But that will just give you a line break in your HTML. If you're trying to get a line break in the displayed text, you should use HTML. For example, you could use:

await UserManager.SendEmailAsync(2, "Confirm your account", 
    "Please confirm your account by clicking this link:<br /><a href=\"www.cnn.com\">link</a>");

... but I gather the <br> tag is mostly out of favour - you should look at other ways of controlling the layout of your HTML. Just remember that a linebreak in the HTML itself is unlikely to be relevant in your page.