The Red C poll in tomorrow's Sunday Business Post also shows that just 22% of voters think Mr Ahern should not have announced his resignation.
The snap Red C poll was carried out on Thursday, just a week since their last poll for The Sunday Business Post.
500 voters were questioned, just half the normal sample, giving a higher margin of error.
Fianna Fáil support, at 40%, is up five points since last week, while Fine Gael drops 2 to 28%, Labour is unchanged at 11, the Greens gain one to 9%, Sinn Féin drops three to six, the PDs are stuck at 1%, and Independents and Others drop two to 5 %.
Asked who would make the better Taoiseach, 63% opted for Brian Cowen, compared to 24% who prefer Fine Gael leader Enda Kenny, and 13% who either do not know, or do not like either option.
22 % of voters thought Mr Ahern should not have resigned, while 31% say they did not want him to go but he had no option after recent revelations.
20% thought it was about time he resigned, and 24% thought he should have gone as soon as the Mahon Tribunal began investigating his affairs.
