You can use a Data URI but there are some limitations. Here's an example, based on my answer to an earlier question. The first thing you'll note is that you can't really control the filename, but it works OK in Firefox and Chrome other than that, but probably not so well in IE (I've not tried it).
Assuming you can already generate the PGN as a string, the code to create a Data URI is quite straightforward:
function exportData(data, target) {
var exportLink = document.createElement('a');
exportLink.setAttribute('href', 'data:application/x-chess-pgn;base64,' + window.btoa(data));
exportLink.appendChild(document.createTextNode('sample.pgn'));
document.getElementById(target).appendChild(exportLink);
}
Just set data with whatever you're generating and set up an element to hold the link once it's created.
In the future we'll have better solutions for this sort of issue, but there's no browser support for it yet.