Because you have no control over the website being shown in the WebView, you are unable to change the type of keyboard that is appearing.
My tests indicate that Android devices will show a "Next" button for every <input type="text" /> or <input type="password" /> field on a website and a "Go" or "Done" button for the last element on the page. If there were some html or css property that could be used to force a different type of keyboard, then you could enable JavaScript in your WebView and execute a JavaScript pseudo url to alter the facebook page's input elements;
WebSettings webSettings = webView.getSettings();
webSettings.setJavaScriptEnabled(true);
webView.loadUrl("javascript://getElement('signinbox').style.someCssClass='someKeyboardProperty';");
However as stated above, I am unaware of any html/css tag that specifies this. Hope this helps!