Javascript Counter

You can do it using this code. You just need to select a stamp of the type that you want to count before running it:

(function () {
   
    if (this.selectedAnnots==null || this.selectedAnnots.length==0) {
        app.alert("You must select a stamp first.");
        return;
    }
    var selectedAnnot = this.selectedAnnots[0];
    this.syncAnnotScan();
    var annots = this.getAnnots();
    if (annots==null || annots.length==0) {
        app.alert("There are no comments in this file.");
        return;
    }
    var counter = 0;
    for (var i in annots) {
        if (annots.type=="Stamp" && annots.AP==selectedAnnot.AP) {
            counter++;
        }
    }
    app.alert("There are " + counter + " stamps of this type in this file.",3);
})();

The code can be executed from the Console, or even from an Action or a menu-item (the latter will require placing it in a folder-level script, though).