var Promise = require("bluebird");
var apiUrls = ["url1", "url2", "url3"];

var request = function(url) {
  // request the rate limited api (returns a promise)
};
var saveResponse = function(response) {
  // save response to file/db (returns a promise)
}

apiUrls.reduce(function(accumulatedPromise, url) {
  return accumulatedPromise
    .then(function() {
      return request(url);
    })
    .then(saveResponse);
}, Promise.resolve()).then(function(){
  console.log("all done.");
});