If your sole purpose is to serve it "the Richfaces way" (it's actually the JSF 2.0 way), then use <h:outputScript>. Put the file in /resources/js/ajax-error.js of public webcontent (the main path /resources is mandatory and its name cannot be changed). Then reference it as follows:
<h:outputScript name="js/ajax-error.js" />
Regardless of its location in the template, it'll be generated into the HTML <head> like follows assuming that your FacesServlet is mapped on *.jsf:
<script type="text/javascript" src="/contextname/javax.faces.resource/js/ajax-error.js.jsf"></script>
But that doesn't offer you EL support! You won't be able to use #{} in that script. Only in stylesheets which are included by <h:outputStylesheet> the #{} is supported in order to locate background images the JSF 2.0 #{resource['logo.png']} way, but nothing more than that.
In your particular case, I'd rather reference #{facesContext.externalContext.requestContextPath} (or its shorter and more popular counterpart #{request.contextPath}) in the HTML <base> tag or some global JS variable or the HTML data attribute. If set as <base>, all relative links will be relative to it, also in JS.
See also: