What are the performance adjustments for a Beechcraft B1900D on a wet runway?
According to the Transportation Safety Board of Canada when they conducted an investigation into a Beechcraft 1900D overrunning a runway in 1997, they found out that the AFM does not include that information you request, nor was it available to the pilots.


  The snow-covered, slippery condition of the occurrence runway differed from the bare,
  dry surfaces on which the AFM data is based.


and


  There were no performance data available to the pilots to determine the aircraft's
  accelerate-stop distance under snowy and slippery runway conditions.


and


  The James Brake Index (JBI) published in the Canada Flight Supplement contains a table which may be used to
  adjust calculated landing distances to compensate for slippery braking conditions. JBI correction factors for
  compacted snow or snow-covered runways range from 80% to 250% higher than hard dry surfaces. Transport
  Canada did not require the manufacturer to provide data on the effects of soft or wet runways, slippery
  runways, or runways containing loose snow on the aircraft's accelerate-stop distances or take-off distances.


How can the aircraft be approved? They say:


  The manufacturer was, as a condition of the aircraft type approval,
  required to determine and supply certain aircraft performance data including the balanced field lengths at
  various take-off weights, temperatures, and altitudes.


I.e., V1 corrections for non-dry runways were (are) not a requirement for the 1900D.

If the AFM you have is current, then it hasn't changed since. If not, then it may be present in the latest AFM. (But I wouldn't count on it, so verify before placing a purchase order.)

You may also look into the aforementioned James Brake Index.