There's a small javascript error causing you grief.
/includes/modules/order_total/ot_coupon.php
line 89:
Change this:
Code:
   'field' => zen_draw_input_field('dc_redeem_code', '', 'id="disc-'.$this->code.'" onchange="submitFunction(0,0)"'),
to this:
Code:
   'field' => zen_draw_input_field('dc_redeem_code', '', 'id="disc-'.$this->code.'" onkeyup="submitFunction(0,0)"'),
Changing this will allow them to just type in the code and press Enter if they've done anything in the coupon-redemption field.