At 1:41 in this clip, Sauron appears to be talking in Black Speech. What is he saying?
Is this in the books?
In the clip, the phrase is an unintelligible soft whisper drowned out by music and the sound of Frodo and Gollum fighting. I agree with Amarth's comment that it is probably supposed to be the Ring's "voice" as we hear a similar breathless voice at other times when the Ring is involved. Alternatively, you may consider all of these utterances of the Ring to really be Sauron working through the Ring.
I found a copy of the script on imsdb.com. There is no dialog between when Gollum says "Precious! Precious!" (at 1:30 in the clip linked in the question) and the time that Frodo and Gollum fall over the edge of the chasm.
GOLLUM still TRIUMPHANT . . . on the edge of the PRECIPICE ... The FIERY LAVA casting an EVIL LIGHT . . . He jumps about in DELIGHT . . .
GOLLUM: Precious! Precious!
(ANGLE ON) FRODO rises slowly . . . his EYES lock on GOLLUM . . . time seems to stand still as each regards the other ...
(CLOSE ON) the RING glinting in GOLLUM'S HAND . . . BEAUTIFUL ... POWERFUL ... EVIL . . .
SUDDENLY! FRODO lunges at GOLLUM ...
FRODO thuds into GOLLUM, lifting him off his feet . . .
(ANGLE ON) FRODO and GOLLUM locked in STRUGGLE plummet over the EDGE OF THE CHASM.
When we are shown the Ring in Gollumn's hand (immediately before Frodo attacks him), the script includes the words "BEAUTIFUL ... POWERFUL ... EVIL . . ." which seem to be part of the stage directions rather than dialog. However, it's possible that it was decided to convey this impression with an incantation.
The breathless words don't seem to be either "beautiful", "powerful" or "evil", but it is always possible that David Salo (the linguist responsible for the movie's dialog in Elvish, Dwarvish and other languages) was called on to translate the words into Black Speech (although a Black Speech word for "beautiful" seems incongruous). If he did translate those words, I can find no record of it. The only example of his Black Speech phrases in the Wikipedia article on Black Speech are
Gû kîbum kelkum-ishi, burzum-ishi. Akha gûm-ishi ashi gurum.
("No life in coldness, in darkness. Here in void, only death.")