In British English we call the reduced version of words 'the weak form'. (Not all words have weak forms, but a lot of common ones do, and most words of 2 or more syllables have weak syllables).
If you google 'weak form in English' you should find some videos, as these are more helpful that having pronunciation written down.
I'll write it here, and it may help.
Should have......can be pronounced should've or (even more commonly) shoulda in phonemes /ʃʊdə/
Could have.......could've or coulda in phonemes /kʊdə/
would have......would've or woulda in phonemes /wʊdə/