How many characters are we talking here?
Maybe use Special Fonts? Like fish, airplanes, geometric symbols?
Example; The secret phrase is ‘One flew over the cuckoos nest’ and the site is Facebook.
Take the first and last letter in each word in the phrase with digits literal and vowels substituted with digits, followed by the last 4 chars in site name shifted up, last char caps.
Final password: 1fw0rt3csnt@nnJ