You can find a pretty god list on Ranker on which you can vote, add songwriters. (iloveclassicrock.com)
Rolling Stone Magazine has his own ranking list which you can find HERE Rolling Stone's 100 Greatest Songwriters of All Time
"The 100 Greatest Songwriters of All Time" is a feature published by the American magazine Rolling Stone in August 2015. The list presented was compiled based on the magazine's music critics, and unlike previous lists the votes came entirely from the magazine's staff. However, it predominantly features American and English songwriters solely of the rock era.[
We're talking, over the course of an entire career, the person who has written the most great songs--the best songwriters of the 20th and 21st century. A few things to keep in mind, songwriting teams are acceptable if they truly worked together (for example, Elton John writing music to Bernie Taupin's lyrics). When possible, as in the case of John Lennon and Paul McCartney, separate them and focus on individual songwriting.
Of course, who would forget one-half of the creative mind of the greatest band to have ever existed, Paul McCartney has surely made his mark on everybody who lived after the Beatles dominated the industry. 
Together with lyricist Bernie Taupin, Elton John has written some of the most beautiful songs ever, ranging from melodic to rock
4 John Winston Ono Lennon[nb 1] (born John Winston Lennon; 9 October 1940 – 8 December 1980) was an English singer, songwriter, musician and peace activist[2] who achieved worldwide fame as the founder, co-songwriter, co-lead vocalist and rhythm guitarist of the Beatles.
The Who had a one-of-a-kind drummer, a brilliant bassist, a towering singer — and their songs featured some pretty impressive guitar playing too. But they would never have gone anywhere if Pete Townshend hadn't developed into an endlessly innovative songwriter.
Before even becoming part of the iconic Simon & Garfunkel duo, Paul Simon had already proven his worth as a solo act. But it definitely paid off that the two had working experience together to deliver some of the most timeless folk cuts in history.
Known as one of the pioneers of the counterculture of the sixties, Bob Dylan was more of a songwriter than a performer himself, although he did pack some charm onstage. Known as a modern-day poet, Dylan effectively changed the way of how pop music progressed through the years.
Admit it, Fleetwood Mac’s most successful era came when Stevie Nicks and Lindsey Buckingham joined the band in 1975. Stevie Nicks, in particular, had a knack for writing lyrics that were accessible yet mysterious to the masses that greatly helped their standing in the scene.
Keef the Riff, the rock guitar genius of the Stones, His songwriting partnership with Mick Jagger is one of the most successful in history. Richards is widely considered one of the greatest guitarists of all time. His career spans over six decades and his guitar playing style has been a trademark of the Rolling Stones throughout the band's career.
While Bob Seger’s rich and deep vocals will ensnare anybody at first listen, his songwriting prowess will leave hearts aching or pumping twice the pace. Seger knows how to relate to the average Joe with his words, becoming a voice for the voiceless in effect
Brian Wilson’s unique approach to making music elevated the Beach Boys’ status as one of the most influential rock bands to ever exist. From working in isolation to being triggered by the Beatles’ work, Wilson’s creativity found inspiration in the oddest of situations.
