It sounds like you want to use the EvaporativeCooler:Direct:ResearchSpecial object in OpenStudio. This object is similar to the EvaporativeCooler:Direct:CelDekPad, which from the documentation,

"... consists of a rigid media evaporative pad, with water recirculated from a reservoir. The evaporative pad provides the area for the adiabatic saturation of the air. While the process provides a lower dry-bulb temperature, the moisture content of the leaving air is higher than the entering condition. The direct stage is used for comfort cooling in a building where adding humidity to the air can be tolerated."

This "research special" evaporative cooler just has a different set of input fields than the "Cel Dek Pad". The "Cel Dek Pad" is not available in the OpenStudio application for v2.6.

UPDATE

After some review with the research special evaporative cooler, it appears that EnergyPlus is currently set up to control outlet temperature of the cooler -- applying a humidity setpoint manager to the evaporative cooler's outlet node has no impact. To get around this, you can apply a temperature setpoint manager to the evaporative cooler's outlet node so that the corresponding outlet humidity provides enough humidification for your needs.