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.");
  });