Currently, you can trigger another build, but not a promotion without some custom groovy and restrictions outlined below:

UI should allow specifying:
- Source configuration
- Whether to use last successful, last build, or build id calculated by script
- Promotion to trigger
- Variables to pass to promotion step

Node selection must be 'server'.

Script:
groovy:
import com.pmease.quickbuild.*
import com.pmease.quickbuild.persistence.*

def confName = 'PATH_TO_BUILD_CONFIGURATION_TO_PROMOTE';
def conf = system.getConfiguration(confName);
logger.info ('Configuration: ' + conf);
def latestSuccessful = conf.getLatestSuccessfulBuild();
logger.info ('Latest Successful Build: ' + latestSuccessful );

def promotionDef = conf.findPromotion('NAME_OF_PROMOTION');
promotionDef = ScriptEngine.instance.installInterpolator(promotionDef);
logger.info ('Promotion: ' + promotionDef);

def variables = [environment:vars.getValue('environment')] // Populate required variables here

Context.push(latestSuccessful)
try {
  promotionDef.promote(latestSuccessful, variables );
} finally {
  Context.pop()
}