Use backslash to escape special characters in JavaScript strings, e.g.
Response.Write(@"<script>window.open('http://www.domain.com/url-with-\'quote','_blank');</script>");
Note that I've also changed the C# string to be a @ string so you don't have to escape the backslash and the quote in the C# code.
I've also changed the URL to a realistic example because as people above have said, a URL with a quote in the domain part is not valid and won't work even if you format the code correctly.