Can someone tell me how to pronounce Quinny and Kwini?

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(For help with the International Phonetic Alphabet (IPA) symbols, see Wikipedia's IPA for English page.)

For me, the Quinny pretty clearly suggests [ 'kʷɪ . ni ]. The spelling of the word is very highly conventional (e.g., the qu sequence and the double n are both found in many English words).

Kwini, on the other hand, is very non-conventional. The spelling makes it seem like a loanword from another language. With that spelling, it is certainly possible to be pronounced the same as Quinny. English spelling is rather flexible, so that can't be ruled out. However, it's also possible to pronounce it as [ 'kʷi . ˌni ] (i.e. something like quee-knee), with the first vowel as [i] (rather than [ɪ]) and a secondary stress on [ni].

I hope this helps!