See this page on the website of Porto Airport:
http://www.ana.pt/portal/page/portal/ANA/AEROPORTO_PORTO_CNT/?AE_PR=193813&actualmenu=184178&cboui=193813
There are no direct buses from Porto Airport to Coimbra.
There is a Rede Expressos bus from Porto to Coimbra at 00:45 arriving at 02:10.
Have a look at this article on my blog as to how to get from the Airport to the bus station.
http://barlaventostravelblog.blogspot.com/2009/01/bus-from-porto-to-castelo-branco.html
