While intrigue continues to swirl around the soon-to-be-vacated Senate seat now held by Hillary Rodham Clinton (D), a new poll suggests that the popularity of one of the leading candidates for the appointment, Caroline Kennedy, is waning.

A Public Policy Polling poll conducted Jan. 3-4 found that in a potential 2010 matchup between Kennedy and Rep. Peter King (R), who has expressed an interest in running in the special election, Kennedy would get 46 percent to King’s 44 percent.

Another leading contender for the Senate appointment, state Attorney General Andrew Cuomo (D), fared much better against King, leading 48 percent to 29 percent in the poll.

The automated survey of 700 registered voters had a 3.7-point margin of error.

Meanwhile, a Gallup Poll conducted Jan. 5 for USA Today found that 45 percent of Americans would like to see Kennedy get the appointment, while 36 percent would prefer someone else. The poll of 1,000 adults had a 3-point error margin.

Gov. David Paterson (D), who gets to name Clinton’s successor assuming she is confirmed as secretary of State, denied reports earlier this week that he was on the verge of announcing his intention to appoint the daughter of the 35th president. Instead, he has asked about a dozen potential appointees to provide him with extensive financial and personal information before he makes a decision.

Two of the House Members who are interested in the appointment, Rep. Carolyn Maloney (D), who lives in New York City, and Rep. Steve Israel (D), who represents portions of Long Island, have traveled to upstate New York in the past few days to meet with local officials and voters, according to media reports.

And in a related development, an anonymous Web site supporting the appointment of upstate Rep. Kirsten Gillibrand (D) to the Senate, SelectGillibrand.com, was launched on Wednesday.