New York Democrats hope they have another candidate to challenge Republican Sen. Alfonse M. D'Amato in John S. Dyson, who served in the cabinet of former governor Hugh L. Carey (D).

The Democrats contend that D'Amato can be beaten, but many doubt that either of their two likely candidates, Mark Green, a public-interest lawyer and former congressional candidate, or Franklin J. Havlicek, an NBC executive, can win. As a result, state party Chairman Laurence Kirwan named a search committee to find a candidate who meets two pragmatic qualifications for victory: that he or she be "reasonably well-known and self-financing," in the words of one party official. Dyson meets those criteria.

Dyson, who served eight years in Carey's cabinet and then as chairman of the New York State Power Commission, has the "necesary money and a pro-business image, is better known throughout the state, is a conservative Democrat and can't be painted as a liberal by D'Amato," according to state Democratic Party Executive Director William Cunningham.

"It's a very complicated decision and I'm considering it at the request of Sen. Daniel Patrick Pat Moynihan D-N.Y. and others I respect," Dyson said yesterday. A Dig on the Canal

So you thought the Panama Canal treaties, which began the process of turning control of the canal over to Panama eight years ago, were a dead issue? Not in the North Carolina Republican primary fight for the seat of retiring Sen. John P. East (R), which matches Rep. James T. Broyhill against David Funderburk, the candidate of the National Congressional Club, which has ties to Sen. Jesse Helms (R-N.C.).

Funderburk is spending $100,000 to run a 30-second ad for a week on every television station in the state. It accuses Broyhill of voting to "pay Panama to take our canal" because he voted to reduce Panama's payments to the United States.

Funderburk says the ads are to counter Broyhill's claim that he is a "good Republican," a "conservative Republican." Wheels Across Iowa

Arizona Gov. Bruce Babbitt likes to bill himself as an "unconventional Democrat" as he explores a 1988 presidential race. His initial foray into Iowa, at least, fits the description. Nearly all the potential 1988 contenders of both parties have already toured Iowa by airplane and automobile. Babbitt is making his first tour in July -- by bicycle.

Babbitt, his wife and two sons will join the weeklong Des Moines "Register's Annual Great Bike Race Across Iowa" (RAGBRAI). Babbitt's press secretary Michael McCurry says Babbitt assures him that he is in "more than fit shape to accomplish the mission, which is make it from one end of the state to the other." Polls

Iowa Gov. Terry E. Branstad (R) is in some political trouble, primarily because more than three-fourths of Iowa's adults say the economy is either somewhat unhealthy or very unhealthy, according to the latest Iowa Poll. The poll shows Branstad slipping four points and his Democratic challengers each gaining four points since the last poll in January. Against his Democratic challengers, Branstad is tied with Lt. Gov. Robert Anderson, at 43 percent each, and leads former Iowa Senate majority leader Lowell Junkins 43 percent to 40 percent.

In the Democratic primary race, the poll shows Junkins leading Anderson by 12 points, with 41 percent undecided.

California Gov. George Deukmejian (R) has nearly tripled his lead -- to 17 points -- over Los Angeles Mayor Tom Bradley (D) in the past two months, according to the latest Los Angeles Times Poll. It shows Deukmejian with 53 percent and Bradley with 36 percent.