Peaceable Projects Inc. is a U.S.-based non-profit group that brings the vast resources of the wide world together with the ongoing needs of the people who live, work, and travel on the Camino de Santiago pilgrim trail network in Spain.
Laurie Reynolds is our resident expert on this route and has written the most up to date guide which is available to download from http://www.csj.org.uk/guides-online.htm She is currently walking the Via de la Plata and I'm sure will correct any mistakes I make when she logs on!
Have a look at what she says about Credenciales, sellos (carimbos) and albergues. Where are you flying into? If you are starting from Lison you can get one at the Cathedral there. If you are arriving in Porto you can get one at the Cathedral there.
I think you will not be able to get a Credencial in Coimbra. There are no albergues on the stretch from Lisbon to Porto and therefore I suspect Porto Cathedral will be the first place you will be able to get a Credencial if you are travelling by some other route to Coimbra to start.
You will only need a Credencial if you intend to sleep in albergues (from Porto on) or if you want to ask if the Bombeiros Voluntarios (Volunteer Firefighters) will let you sleep on the floor. They may help in this way but acording to the Guide don't provide mattresses but may provide showers. However there is ample low cost private accommodation available.
If you want to simply keep a record of the few stages from Coimbra to Port - when you can get a credencial - or sleep in the Firestations from Coimbra - I'd simply make my own credencial in which to collect carimbos and thenuse the "official" credencial from Porto onwards. I've done this several times and if you PM me I can send you a sample.