This very brief rehearsal footage turned up in 2015 from the AP archive which filmed the rehearsals for the Music for UNICEF - A Gift of Song Concert for the press.

ABBA were not wearing the same clothes as for the WCBS News Report, so this was probably filmed on the day of the concert itself in the morning of Tuesday 9 January 1979.

In response to a question about more information or footage, AP archive confirmed that unfortunately this 1 minute footage is all that remains.

Click here for a picture from rehearsals.

Broadcast information:
9 or 10 January 1979, NBC, USA (probably teasing the TV broadcast), USA
10 January 1979, NOS, The Netherlands

A lady in the all-star line-up who looks a lot like tennis player Billie Jean-King standing next to Andy Gibb.  I don't think it is her - she's probably just a stand-in for the only big name in the line-up seemingly not present at this rehearsal (and who didn't appear to know the words in the actual concert!) - Rod Stewart.

Music for UNICEF - A Gift of Song Concert Rehearsals, 1979;
Music for UNICEF - A Gift of Song Concert, 1979; 

Archive data from AP archive:
Title: SDUSA UNICEF POP CONCERT
Summary: SYND 10 1 79 POP SINGERS REHEARSING FOR CONCERT IN AID OF UNICEF
Story No: z040339
Source: AP Television
Aspect Ratio: 4:3
Date: 09/01/1979 00:00 AM
People: Olivia Newton-John, Andy Gibb, John Denver

Archive data from Beeld en Geluid:
DOCID: 77149
COLLECTIE: Televisie Journaal
TITEL: JOURNAAL
ZENDGEMACHTIGDE: NOS
UITZENDDATUM: 1979-01-10
BEGIN-EINDTIJD: 00:32:00 - 00:33:00
DRAGERNUMMER: TD14441 {DIGI-BETA}
V51 {VHS}
GENRE: journaal
BESCHRIJVING: Popconcert tbv Unicef in grote zaal van VN 60"
TREFWOORDEN: popmuziek
PERSOONSNAMEN: Newton-John, Olivia
NAMEN: Abba; Unicef; VN
TECHN-GEGEVENS: Materiaal: Kleur

Thanks to Jozsef.
YouTube link c/o AP Archive