That's happening because you're using a relative path for the buttonImage property.
Instead, use an absolute path and the problem will be solved.
eg:
$.datepicker.setDefaults({
showOn: "both",
buttonImage: "/myapplication/images/Calendar.png",
buttonImageOnly: true,
buttonText: "show calendar"
});
(In practice, I usually have a javascript variable defined which contains the application root and then combine that with the path to a resource: that way if the application has to be deployed to a different path, all the images don't break.)
eg:
var appRoot = '<%=Request.ApplicationPath%>';
$.datepicker.setDefaults({
showOn: "both",
buttonImage: appRoot + "/images/Calendar.png",
buttonImageOnly: true,
buttonText: "show calendar"
});