Postman JS Pre-request script for dynamic dates.

PreRequestScript.js

var moment = require('moment');

// Allows dates to be offset in the past rather than right now. offset format "hh:mm:ss".
// "24:00:00" would be 24hrs in the past.
var offsetValue = pm.globals.get("offset");
var offset = moment.duration(offsetValue);

// Determines the duration between start & end dates format "hh:mm:ss"
// "00:30:00" would be a 30 minute delay.
var durationValue = pm.globals.get("duration");
var duration = moment.duration(durationValue);

// Calculate
var startTime = moment().subtract(offset).subtract(duration);
var endTime = moment().subtract(offset);

// set for reuse in the request, these could be globals or environment variables. They're always recalculated on a new request.
pm.environment.set('startTime', startTime.format());
pm.environment.set('endTime', endTime.format());

RequestBody.json

// With my current understanding, quotes are required otherwise date is not outputted as a string literal
{
  "StartDate": "{{startDate}}",  
  "EndDate": "{{endDate}}".
  //.. Some other data
}