I love this tune! The Real Book has the third chord as an Ab7, though the majority of recordings I’ve found seem to prefer a D-7. I wouldn’t say the Ab7 is necessarily “wrong” though, as several some recordings use the Ab7. Learn to navigate both, and use your ears at jam sessions!
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Videos to learn the melody/changes
Sonny Stitt Quartet - There Is No Greater Love
05:09
There Is No Greater Love/The One Before This - Ammons and Stitt
13:51
Oscar Peterson with Ray Brown and Niels-Henning Ørsted Pedersen - There Is No Greater Love
06:19
John Scofield There Is No Greater Love
03:45
Billie Holiday - There Is No Greater Love (Decca Records 1947)
03:01
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Saw Scofield live, it was incredible.
Luckily, if the band you are playing with does play the D-7 as the third chord and you are playing the Ab7, you’ll be blowing over it as the tri-tone sub, and it could sound really hip.
You are close but not really spot on I guess. There is no tritone in D-7. Tritone subs are just that – they work for dom chords because 2 dom chords a tritone apart both have that tritone present. In D-7 you have a natural F while in Ab7 there is Gb=F# so they are not the same interval.