A closer look
Should recommends or expects something. Could offers a possibility or a polite option. We should move the meeting sounds like advice; We could move it floats the idea without pushing it. Both can work when you only want to nudge.
Compared options
We could apologize. It suggests one possible path and leaves the choice open.
We should apologize. It tells the reader you think it is the right thing to do.
You could reply tomorrow. A soft, friendly reminder.
You should reply tomorrow. The same reminder, slightly firmer. In a nudge like this, either fits; only tone differs. The pair above changes one word each, so the meaning shift stays easy to hear.