I usually put the CSS into the stylesheet, but to make it easier, I've included it in the div code:
<div align="left" style="border: 1px solid #CCCCCC; width: 350px; padding: 10px; background-color: #EEEEEE; margin-top: -160px;">
{include file="modules/Discount_Coupons/add_coupon.tpl}
</div>
That will create a shaded box with a border, and offset it 160 pixels in the 'up' direction. Be very careful with negative margins, as IE and Firefox render them very differently. Test it out on all browser/OS combinations. This can go anywhere after the closing </form> tag in cart.tpl.