This is a pretty ambiguous question - do you include those bands in which only one or two members were the main songwriters? Lennon-McCartney and Jagger-Richards would be the most obvious example of this.
Leiber & Stoller were a production and songwriting team who, in addition to Presley and the Coasters (already mentioned), were also closely associated with the Drifters and, IIRC, they were the producers for many of the Coasters and Drifters recordings.
I would also add the following:[ul]
[li]Ben Mink - songwriting partner with k.d. Lang[/li][li]Bob Dylan - Joan Baez (though Baez was doing it to promote Dylan but she became known as a Dylan “interpreter”[/li][li]Bob Dylan - Byrds[/li][li]Dave Alvin - Blasters (though he was a member of the group)[/li][li]Holland-Dozier-Holland for the Temptations & Supremes[/li][li]William “Smoky” Robinson - same as above[/li][li]Doc Pomus & Mort Shuman - Elvis[/li][li]Brill Building writers (King & Goffin, etc.) who wrote many of the pop songs for period of 1960 to 1963[/li][/ul]
[Nitpicking]
I would not include this association for two reasons: [ul]
[li]Strayhorn was Duke’s arranger and was a full time member of the orchestra for many years. [/li][li]Throughout Strayhorn’s entire run with Duke, Ellington was, without a doubt, the main song writer for the orchestra and therefore the songwriter name that would be associated with orchestra.[/li][/ul]
I believe the same could be said of the relationship between Oliver and the Lunceford Orchestra along with Fletcher Henderson and Basie, etc./[Nitpicking]