I will be there on a Sunday from 10am to 6pm. I don't know where the ship will dock. The ship will be coming from the US and this is the first stop. I appreciate any suggestions.The only ship I see on the port schedule coming from the US on a Sunday in April is the Sillhouette, on April 29. If that is your ship, it will be at the Alcântara terminal, and is scheduled for mooring at 8am. So if indeed they pull up alongside at 8am, 2 hours for Schengen clearance should be plenty, and you should be off the ship at 10am or even earlier.
As the ship sails in (and out) of the harbor, it passes the Belém area. So if you are up and about (should be at 7:30am or so) you can see the tower and some monuments from the ship. Nothing like being there, though, and you certainly won't get any custard pastries as you sall by.
On Sundays there is little traffic in Lisbon, and there is nothing special going on on 4/29 that I know off that would create any travel disruption. So you are in good shape.
You may want to know that government-owned monuments and museums are free on Sunday mornings, until 2 pm. For savings, try to hit those first. Museu do Azulejo, Tower of Belém, Discoveries Monument, Jerónimos, and many other are included in this "free on Sunday mornings" deal.
I think if you don't dally you can do both the castle/Alfama and the Belém areas. However, if you like to take it leisurely, explore in more depth and take a nice long lunch, you may have to stick with one area. I would recommend you start with whichever of the two areas interests you the most, and when you are done if there is time go to the other. They are about 20 minutes apart, and each about 10 minutes from the Alcântara terminal. All times by taxi or private vehicle.
I hope this helps. Let me know if you have any other questions.