The Conservative Party of New York has been the minor party that runs candidates in the largest share of its state’s legislative seats, compared to any other minor party. This has been true continuously starting in 1970. The Conservatives hit their peak (for number of legislative nominees) in 1982, when the party had nominees on the ballot in over 92% of New York state’s legislative races (195 nominees out of 211 races).
However, there are signs that the Conservative machine is flagging slightly. In 2008, it had nominees in only 149 legislative races (out of 212 races). That was the lowest number it had run since 1964. Meanwhile, the Working Families Party of New York is gaining. In 2008 it ran nominees in 142 legislative races, its best showing so far.
Of course, since these two New York parties mostly cross-endorse Republican or Democratic nominees, the two New York minor parties have an easier time with candidate recruitment than most minor parties do. Still, it is always a sizeable amount of work to place that many nominees on each party’s primary ballot.