There are only two trains that leave from Obidos to Coimbra on March 28th. I cannot seem to find a way to buy these tickets in advance. Can you just show up to the train station on the same day and buy your ticket? Or does this mean that they are sold out? I was able to purchase my other train tickets in advance. Any tips or advice would be greatly appreciated!
You can't buy this in advance as Portuguese rail only sells tickets online for journeys using Alfa Pendular or Inter-City long-distance services. This journey only uses regional and local trains, so you will have to buy the ticket at the station. No need to do it in advance, local trains of this kind don't "sell out" - in the remote chance that all the seats are occupied you can get on and stand.
Also my search on the Portuguese rail site suggests that there aren't two trains between those destinations, but two itineraries that don't require excessive time waiting around for connections. You will change twice, at Caldas de Rainha and Coimbra B (the long-distance station that is outside Coimbra city centre).
This is very helpful. Thank you so much Phillip!