I'm not sure as well. This is a fixed expression for being pregnant. It can be genitive or dative. I always thought it being a partitive usage of genitive meaning we have some good hope. In older literature there are many examples for this usage. Sie tranken viel guten Weines (plenty of). Now having had a closer look on it I rather think that it is an instrumental usage of genitive which
is also quite elaborate but a little bit more common nowadays. So it would mean something like "we are carrying;with". In this sense I would understand it even in not idiomatic expressions. Guter Hoffnung stiegen wir in die Höhle (with best expectations we entered the cove). Other examples of that usage. Guten Gewissens kann ich dem nicht zustimmen. Langsamen Schrittes näherte er sich. Sehenden Auges rannte er in sein Verderben. Most of these examples would be expressed with dative (and mit) in a more up to date version. Mit gutem Gewissen kann ich dem nicht zustimmen. Mit langsamem Schritt (or better, mit langsamen Schritten) näherte er sich.
I've never heard being pregnant in plural, even in cases like "All of my friends are expecting a baby" Alle meine Freunde sind guter Hoffnung.