Tampermonkey filesave dialog

gistfile1.txt

A very fast and easy solution is to use FileSaver.js :
1) Add the following line into the ==UserScript== section of your Greasemonkey script

// @require     https://raw.githubusercontent.com/eligrey/FileSaver.js/master/src/FileSaver.js
2) Add the 2 following lines of code to the GM script

var blob = new Blob(["Hello, world!"], {type: "text/plain;charset=utf-8"});

saveAs(blob, "hello world.txt");

This code example will display a dialog box to download a file named "hello world.txt" containing the text "Hello, world!". Just replace this by the file name and the text content of your choice !