Unfortunately, there isn't any good rule as far as I know for whether "-se" after a vowel is pronounced as /z/ or /s/ ("-se" after a consonant is almost always /s/, with only a few exceptions like cleanse).
Nouns, verbs and adjectives spelled with "-se" may end in either /s/ or /z/. As you have observed, there are some noun-verb pairs where the noun has /s/ and the verb has /z/ (e.g. "excuse") but this is not a consistent pattern, even for words that come in such pairs: "base" is pronounced with /s/ as both a noun and a verb, and "pose" is pronounced with /z/ as both a noun and a verb. (A side note: some noun-verb pairs have a spelling change as well as a pronunciation change, like advice/advise and device/devise.)
Nouns with the "-Vse" spelling pattern seem to me to be almost evenly split, or maybe even a bit more likely to have /z/ than /s/: we have /s/ in abuse base caboose case chase crease dose excuse goose grease grouse house lease louse moose mouse noose release use and vise (a US variant spelling of vice, in the sense "clamp") and /z/ in applause bruise cause cheese clause cruise demise disease disguise ease fuse guise hose muse noise nose pause phase phrase poise pose praise prose raise rise rose ruse surprise tease. A few "-Vse" nouns can be pronounced with either /s/ or /z/: spouse, blouse, and vase.
There are more "-Vse" verbs ending in /z/ (like braise lose choose diffuse infuse peruse amuse devise advise revise comprise rise arise excise close transpose propose expose impose oppose please ease appease cause (a)rouse) than there are ending in /s/ (chase debase encase/incase cease release crease grouse loose) but either sound is possible. A few verbs can be pronounced with either /s/ or /z/: erase douse dowse grease.
In British English, the spelling -se is used for more verbs than in American English. The verb practise (American English practice) corresponds to the noun practice and is typically pronounced the same, despite the spelling difference: /ˈpræktɪs/, with /s/. Verbs ending in the suffix -ise, such as realise (American English realize) are pronounced with /z/.
For adjectives with the spelling "Vse", /z/ occurs in wise, but I think most others have /s/ (like loose close obtuse diffuse obese concise).
I wasn't aware of this before Mitch left a comment, but apparently adjectives ending in the suffix -ese (such as Japanese, Portuguese) can be pronounced with either /s/ or /z/.
The Oxford English Dictionary says that adjectives ending in the suffix -ose also show some variation between /s/ and /z/: "The traditional pronunciation has /s/, but /z/ is frequently heard in the commoner words of this type, especially where the stress is not on the termination."
Additionally, there are some adjectives from nouns ending in -se /z/ that also end in /z/: rose and turquoise.