tern.jqueryapi provides a tern plugin for jQuery UI.

After installing and converting your project as Tern Project (see Tern-Eclipse-IDE), open Project Properties, click on Tern / Modules item and select the jQuery UI tern plugin (ECMAScript, Browser and jQuery tern plugin must be selected too) :

Completion

After that you can benefit with jQuery UI completion :

Completion for options properties is available too :

Web Browser

You can play with online demo which uses CodeMirror (inside Web Browser).