The trio, who are playing in New York this week, are favourites to be the critics’ choice for their self-titled album.
Other runners for the Irish Album of the Year include Lisa Hannigan’s Sea Sew and Fight Like Apes’ album Fight Like Apes and the Mystery of the Golden Medallion.
The award ceremony will be held in Vicar Street on Wednesday, March 4, and the winning act will receive €10,000.
The Irish equivalent to the Mercury Music prize, the Choice award winner is selected by a panel of media professionals drawn from print, radio, TV and online sectors across Ireland.
Instead of using sales or airplay as criteria, the Choice judges focus on the music and select an album which best represents Irish musical talent from the year.
Paddy Power spokesperson Sharon McHugh said: “While this award usually tends to go to an outsider in the betting, we just couldn’t discount The Script. 2008 was a phenomenal year for the trio.”
Previous winners include Julie Feeney, who won the inaugural prize for 2005, The Divine Comedy and Super Extra Bonus Party.
The Script is favourite to scoop the prize at 3/1.
Lisa Hannigan and Fight Like Apes are 9/2, Jape (Ritual) 5/1, David Holmes (The Holy Pictures) 7/1, Mick Flannery (White Lies) 8/1, Halfset (Another Way of Being There) 10/1, Messiah J & The Expert (From The Word Go) and Oppenheimer (Take The Whole Mid-Range And BoostIt) 12/1 and RSAG (Organic Sampler) at 16/1.