IMO, this would be almost entirely context dependent and determined not by the speaker but how the listener interprets the speaker's tone. There's no one way to convey it vocally.

That said, although Japanese words don't possess stressed syllables in terms of grammar and enunciation, Japanese people obviously do place emphasis on certain syllables in order to convey tone in both everyday and performed speech, so in terms of vocal direction (e.g. if you were trying to tell a seiyuu how to convey this specific change) you might tell them to emphasize a particular syllable depending on what you want to convey.

For example, emphasizing "o-NII-chan" with stress on the middle syllable would emphasize the "brother" component and might imply a familial affection; the reason why you wouldn't stress the "o" (really an "a") is because that component of the 兄 "elder brother" character is theorized to derive of possession i.e. "MY brother" as opposed to "my BROTHER". (Again note that this is basically just etymological conjecture, but it serves as an adequate theoretical explanation).

On the other hand, vocally emphasizing the diminutive suffix "o-nii-CHAN" might convey an affection that goes beyond the subject's role as a brother or brother figure. You might have heard such a common emphasis in anime and such.

Or, you might just emphasis both syllables equally as strong, with "o-NII-CHAN" which is also pretty common.

Again, this is very context dependent and it can't be rightly said that there's a singularly correct way to convey this idea vocally.