Why does child sometimes become a two-syllable word?

I think you mean that it is actually a tripthong, the "i" being pronounced as a dipthong (ai) and a schwa added afterwards, Presumably a wild child is two tripthongs.

When a word ending in a vowel comes at the end of an utterance, it tends to be longer than when it is followed by a consonant, and longer when followed by a voiced consonant than by a unvoiced one. [See Cruttenden(2001.95), Gimson's Pronunciation of English'] A spectrogram will show that the bolded vowel of [1] below is longer than that in {2], which is longer than that in [3].

1. John likes me.

2. John likes mead

2. John like meat.

For some speakers in British English, child is pronounced as a two-syllable word. For most speakers, both of the one- and two-syllable versions, the /d/ of child is not released when the word ends an utterance, and for some it is not audible at all. This means that the diphthong or triphthong of utterance-final child is longer and the second syllable (for those who produce it) more evident than when child is immediately followed by another sound, as in child abuse.

Interestingly, the Longman Pronunciation Dictionary lists the two-syllable version as an optional pronunciation of child, mild, mile, wild, while etc, but the Cambridge English Pronouncing Dictionary does not.

Not sure if this is linked at all to the New York dialect I grew up with, but if pressed I would likely respond that "child," "fire," and "owl" all seem to have two syllables.

As a rule in correct post 19th century English pronunciation, a word ending with the consonants "ld" where the L is silent, is pronounced as a one syllable word - as in the word "could"; but a word ending with the consonants "ld" where the L and D are enunciated together and the vowel preceding the "ld" is a long vowel, then it becomes a two syllable word such as the word "child". Which means in correct modern English pronunciation, the combination of the two words "child abuse" is four syllables, not three, and if any English speaker speaks the word "child" as one syllable, then they are not pronouncing this word correctly regardless of how many words are used in conjunction or in combination with that particular "ld" word with the long vowel preceding the "ld" consonants, and regardless of whatever dictionary says how to pronounce these particular "ld" words with the long vowel.
This rule applies to correct American English and correct British English. There is always the issue of dialects for English speakers throughout the world (actually for any language) and these dialects have historically taken on pronunciations of words that are particular to that dialect, that is not to say that it is the correct pronunciation because often it is not, which happens to be the meaning of dialect - dialect actually means a variance of a correct pronunciation of words and their usage, and always has its origin as a regional characteristic of linguistics, which is why there is the major problem of people's speaking the same language who cannot understand each other because of their dialects, all languages have this dialect problem.

The number of syllables depends on the pronunciation. It has nothing to do with spelling.

According to the OED:

A syllable is a vocal sound or set of sounds uttered with a single effort of articulation and forming a word or an element of a word; each of the elements of spoken language comprising a sound of greater sonority (vowel or vowel-equivalent/vowel-like) with or without one or more sounds of less sonority (consonants or consonant-equivalents/less sonorous).

A simplified version of the OED definition is: a set of (one or more) sounds including at least one vowel-like sound and possibly with other consonant-like sounds surrounding it.

Technically the number of syllables is determined by the peaks of sonority.

The only common exception is a cluster of /s/ followed by a stop (i.e. /st/, /sk/, /sp/ etc).

Now Sonority hierarchy and Sonority sequencing principle (SSP) come into play.

The typical sequence of SSP is:

Vowel > Glide > Liquid > Nasal > Obstruent.

Vowels are the most sonorous and obstruents are the least sonorous sounds.

Now if you pronounce child [t͡ʃaɪ̯ld̚], then there is only one peak of sonority here, hence one syllable.

If you pronounce child [t͡ʃaɪ̯əld̚] or something like that, then there can be two peaks of sonority which means two syllables.

I can't draw the Sonority graphs for the pronunciations I mentioned above but I will upload two graphs I've made earlier.

• Metal -> [me.tl̩]
• Melt -> [melt]

Both 'metal' and 'melt' have the same sounds but in different order. How many syllable do you think each has? Let's draw a sonority graph to see:

There are two peaks (indigo colour) of sonority (one peak by the vowel [e] and another by syllabic l [l̩]) in the word metal, so it has two syllables.

There's only one peak of Sonority in 'melt', so one syllable.

See Wikipedia on Phonology:2 Y-cluster reductions - 2.1 Yod-dropping, and 2.2 Yod-coalescence

The OED gives:

Child

Pronunciation: Brit. /tʃʌɪld/, U.S. /tʃaɪld/

Inflections: Plural children Brit. /ˈtʃɪldr(ə)n/, U.S. /ˈtʃɪldr(ə)n/

However, in parts of the UK, there is an intrusive (or linking) yod that creates two syllables /'tʃjʌɪ.jʌld/ and /ˈtʃjʌl.dr(ə)n/

See the website English Pronunciation Roadmap

The second is a ‘y’ sound as in ‘yet’. For example, ‘she opened’ sounds more like ‘she-y-opened’, ‘she-y-opened’ can you hear that? It’s more like ‘yopenned’, ‘she-y-opened’. And ‘I asked’ sounds more like ‘I-y-asked’, ‘I-y-asked’.