Since you are looking for something stable, the merge sort should do.

http://en.literateprograms.org/Merge_sort_(JavaScript)

EDIT:

According to this post, it looks like Array.Sort in some implementations uses a merge sort.

It is possible to get a stable sorting from a non-stable sort function.

Before sorting you get the position of all the elements. In your sort condition, if both elements are equal, then you sort by the position.

Tada! You've got a stable sort.

I've written an article about it on my blog if you want to know more about this technique and how to implement it: http://blog.vjeux.com/2010/javascript/javascript-sorting-table.html

Will the built in sort function do? http://www.w3schools.com/jsref/jsref%5Fsort.asp

Check this article:

http://www.hedgerwow.com/360/dhtml/js%5Farray%5Fstable%5Fsort.html

It seems that only FF 2.0 and Opera 9 and earlier have a non-stable sort implementation. All other mainstream browsers do.

You should be able to utilize the core Array.sort method. Example...

var data = []; //populate array

function sortByName(a, b) {
  var x = a.LastName.toLowerCase();
  var y = b.LastName.toLowerCase();
  return ((x < y) ? -1 : ((x > y) ? 1 : 0));
}

data.sort(sortByName);

Note: this only sorts ascending. But you can take care of that by tweaking the function or using Array.reverse.