Syllabic consonants are 5: syllabic/n/, /m/, /l/, /r/ and the velar nasal (ing).
Syllabic /l/ can be found after frivative sounds except the lenis post alveolar, never after the aproximants /j/ /w/ /r/, the glottal fricative /h/ and after the affricates. Syllabic /l/ it's possible found after all the plosives and the nasals except the velar nasal.
Syllabic /r/ its most common in American English; before and after /l/, before /n/, before/g/ and after /t/. In BBC you can find syllabic /r/, but must be another consonant after.
Syllabic /m/ and the velar nasal (ing), *both can occur as a syllabic, but only as a result of processes such assimilation and elision. for example, "Rob and Mary", after and, the consonant is bilabial, so we asimilated the same place of articulation.
Syllabic /n/ NEVER found after the affricates, nasals, /h/ an the aproximants.
Now, we pronunce words like London, Minton, abandon, etc, with schwa becouse the clusters nasal+ plosive+ syllabic nasal are very unusual.
*Roach, Peter (1983) English Phonetics and Phology, a practical course, third edn, Cambidge University Press.