Yes, there is a stressed syllable rule for pluralizing nouns in English: do nothing with the stress you didn’t already do in the singular.
The word begonia does ɴᴏᴛ rhyme with Crimea, diarrhea, or the female given name Maria. Instead begonia rhymes with the female given name Sonya, as heard in U.S. Supreme Justice Sonia Sotomayor.
That means it normally has three syllables with stress on the penult: /bəˈɡonjə/. So when you make begonias in the plural it’s simply /bəˈɡonjəz/ with the same stress because inflection never shifts a noun’s stress pattern in English. (Remember that in the International Phonetic Alphabet, the letter /j/ represents the consonant heard at the start of the English word yes.)
However, exactly where you choose to put the syllable break between the stressed syllable and the last one is a matter more of convention than of science.
If you believe in unchecked open syllables, it would be pronounced /bəˈɡo.njəz/ — and I bet the justice herself would say [bəˈɡo.ɲəz] there.
The middle syllable is pronounced like the word go and everything else is in that last syllable — which is therefore just "nyuh" if you're into that silly sort of spelling pronunciation. Think of it sounding a bit like this might be said:
Maaan, sheez so ginna owe-nya, dood!
Even if you mean hyphenation for line breaks and not actual speech, it would still be written with hyphens as be-go-nias because those are only two places where you are supposed to break up that word to continue it on the next line in typeset text.