From https://developers.facebook.com/docs/games/requests/v2.0

RequestsDialog.java

    Bundle params = new Bundle();
    params.putString("message", "YOUR_MESSAGE_HERE");

    WebDialog requestsDialog = (
        new WebDialog.RequestsDialogBuilder(getActivity(),
            Session.getActiveSession(),
            params))
            .setOnCompleteListener(new OnCompleteListener() {
                @Override
                public void onComplete(Bundle values,
                    FacebookException error) {
                    if (error != null) {
                        if (error instanceof FacebookOperationCanceledException) {
                            Toast.makeText(getActivity().getApplicationContext(), 
                                "Request cancelled", 
                                Toast.LENGTH_SHORT).show();
                        } else {
                            Toast.makeText(getActivity().getApplicationContext(), 
                                "Network Error", 
                                Toast.LENGTH_SHORT).show();
                        }
                    } else {
                        final String requestId = values.getString("request");
                        if (requestId != null) {
                            Toast.makeText(getActivity().getApplicationContext(), 
                                "Request sent",  
                                Toast.LENGTH_SHORT).show();
                        } else {
                            Toast.makeText(getActivity().getApplicationContext(), 
                                "Request cancelled", 
                                Toast.LENGTH_SHORT).show();
                        }
                    }   
                }
            })
            .build();
    requestsDialog.show();