In Perl Tk the trick is that you can set the 'insert on time' of a text widget to 0, which has the effect of turning off the blinking cursor:
$self->{status_line}=$self->{status_frame}->Text(
-width=>80,-font=>[-size=>10],-height=>1,
-insertontime=>0)->pack(-side=>'left');
Is there an equivalent of this in Java to turn off the blinking cursor?