During the first two years of life, human infants produce increasing numbers of speech-like (canonical) syllables. Both basic research on child speech development and clinical work assessing a child's pre-speech capabilities stand to benefit from efficient, accurate, and consistent methods for counting the syllables present in a given infant utterance. To date, there have been only a few attempts to perform syllable counting in infant vocalizations automatically, and thorough comparisons to human listener counts are lacking. We apply four existing, openly available systems for detecting syllabic, consonant, or vowel elements in vocalizations and apply them to a set of infant utterances individually and in combination. With the automated methods, we obtain canonical syllable counts that correlate well enough with trained human listener counts to replicate the pattern of increasing canonical syllable frequency as infants get older. However, agreement between the automated methods and human listener canonical syllable counts is considerably weaker than human listeners' agreement with each other. On the other hand, automatic identification of syllable-like units of any type (canonical and non-canonical both included) match human listeners' judgments quite well. Interestingly, these total syllable counts also increase with infant age.