In my 16th edition Cambridge English Pronouncing Dictionary, it says, in the introduction,
although native speakers may well find no difficulty in dividing words into syllables, it seems that learners of English have trouble in doing so, . . .
No completely satisfactory scheme of syllable division can be produced - all sets of ruls will throw up some cases which cannot be dealt with properly.
It then describes the 'Maximal Onsets Principle' as follows:
where possible, syllables should be divided in such a way that as many consonants as possible are assigned to the beginning of the syllable to the right rather than to the end of the syllable to the left. However, when this would result in a syllable ending with a stressed /ɪ/, /e/, /æ/, /ʌ/, /ɒ/ or /ʊ/, it is considered that this would constitute a violation of English phonotactics, and the first (or only) intervocalic consonant is assigned to the preceding syllable; thus the word 'better' is divided /'bet.ər/. In the case of unstressed short vowels, /e/, /æ/, /ʌ/ and /ɒ/ are also prevented from appearing in syllable-final position; however, unstressed /ɪ/ and /ʊ/ are allowed the same "privilege of occurrence" as /ə/ when a consonant begins a following syllable, and may therefore occur in final position in unstressed syllables except pre-pausally.
The dictionary puts the syllabic boundary after the p in happy.