There's approximately 47 rap records from 1979.
The thing about King Tim III is that it was released on an established label that kept records of when the music was released and have the paperwork to prove it. A lot of the records listed below were released on an independent label (really just somebody paid $500 to make 500 copies and didn't keep the receipt). As a result, the first rap song that you can prove was King Tim III. People in the know agree that King Tim III was released before Rapper's Delight.
King Tim III and Rapper's Delight both got played on the radio. King Tim III wasn't that popular, but it charted on Billboard as did Rapper's Delight. Many of the songs posted below didn't get played on the radio, didn't chart on Billboard and whoever paid to have the record pressed doesn't have the receipt so there's no proof of when they were released.
Anyway, below is a list of all the records that I know of from 1979;
Rap Records From 1979
1. Rapper's Delight - The Sugar Hill Gang
2. King Tim III (Personality Jock) - Fatback Band
3. Rappin' and Rocking the House - Funky Four Plus One
4. Christmas Rappin' - Kurtis Blow
5. Superrappin' - Grandmaster Flash & The Furious Five
6. To the Beat Y'All - Lady B
7. We Rap More Mellow - Younger Generation (Grandmaster Flash &F5)
8. Rhythm Talk - Jocko
9. Rhymin' and Rappin' - Paulette and Tanya Winley
10. Rap-O, Clap-O - Joe Bataan
11. Lady D - Lady D
12. Jazzy 4 MCs - MC Rock
13. Rhapazooty in Blue - Sicle Cell and Rhapazooty
14. Spiderap/ A Corona Jam - Ron Hunt/Ronnie G & The S.M. Crew
15. Looking Good (Shake Your Body) - Eddie Cheeba
16. Funk You Up - The Sequence
17. Street Talk (Madame Rapper) - Funky Constellation
18. Wack Rap - Solid C, Bobby D & Kool Drop
19. Rapper’s Delight/Rocker’s Choice - Xandu & Sweet Lady
20. Spoonin Rap - Spoonie G
21. Doctor Love & Sister Love - Doctor Love & Sister Love
22. Scoopy - Scoopy Rap
23. Tricky Tee Rap - Troy Rainey
24. Cloud One - Patty Duke
25. Gangster Rock - Little Starsky
26. Willie Rap - Willie Wood & Willie Wood Crew
27. Family Rap - Family
28. Party Rapp - Mr Q*
29. The Rocketship - Jocko
30. Reasons To Be Cheerful part 3 - Ian Dury & The Blockheads
31. Ladies Delight - Mr Q*
32. DJ Style - Mr Q*
33. Rapping Time - Mr Q*
34. Body Rock - Neil B
35. And You Know That - TJ Swan
36. Boogie Beat - Uno
37. Move Your Body - Bramsam
38. Rock Don’t Stop - Taxie
39. I Ran Iran - David Lampell
40. Everybody Here Must Party - Direct Current
41. Can You Do It (Superman)/Back To Metropolis - Dr Superman & Lady Sweet
42. Rappin Blow - Kurtis Blow
43. Lil Beady Eyed Sam - Patron Of The Arts
44. Christmas Delight - The J.P.C. Gang
* Mr Q released four rap records in 1979. Although for some reason he gets no recognition. His name never comes up in a conversation about old school Hip Hop.
Honorable Mentions:
Take My Rap...Please - Steve Gordon & The Koshers (1979)
The Guardian Angel Is Watching Over Us - Golden Flamingo Orchestra (1979)
Fly Guy - Fly Guy Rap (year unknown)
Big Foot Boogie - Brisko The Kidd (year unknown)
A Game Of Life - Lavaba & E. Mallison (year unknown)
Roller Rink Funk - Shift (year unknown)
Ah! Bam Bam Just Jam - Sugar Baby Weet and Filmworks (year unknown)
Green Ribbons - Sugar Baby Weet (year unknown)
Dancing Heart - Universal Two (year unknown)
Smooth Talk - Mr Fox (year unknown)
Enterprise (Runaways Soundtrack -1978)
Potential songs from 1979 with no mp3
1. Unbelievable DJ - Brandy & Hart feat Perris DJ
2. Rappin It Up - First Class
3. Baya Latinos PJ Labor
In my opinion, the best Rap records from 1979 are;
1. Rapper's Delight - Sugarhill Gang
2. Christmas Rapping - Kurtis Blow
3. Rapping & Rockin The House - Funky 4 + 1
4. Superrapin - Grandmaster Flash & The Furious 5
5. Rhymin & Rappin - Paulette & Tanya Winley