Santarem to Coimbra, as suggested above, has some long stretches without accommodations. There is a wonderful hostel in Tomar, a city with a World Heritage Site, but otherwise, many of the smaller villages that dot the way don't have much to offer in the way of beds. I walked CP in Sept 2018, right in the midst of a heat wave (40 degrees C for a few days) and averaged 35KM/day, but found that several fellow pilgrims were taking the bus to make it from albergue to albergue in that stretch. One town, Vale de Figueira, has a train station, outside of town, and a wonderful restaurant/bar, but no sleeping accommodations. I'd of stayed there on one of the hottest days, but took a taxi to Azinhaga instead. Azinhaga (or the surrounding area) also could use at least one more good sleeping place, IMO.
In the opinion of my friends from Lisboa, the Portuguese along the CP are about ten years behind the Spanish in figuring out the commercial potential of having a lot of pilgrims walk the CP, so I expect more hostels/albergues to open in the future.
Good luck and Buon
Between Santarém and Coimbra are lots of acommodations
Golegã ,Ansião , Tomar Rabaçal ,Cernache etc everywhere you can stay within 20 kms.