There are four diphthongs in Modern Persian:

āy is a glide very close to–and slightly more open than–/i/ in English ‘bite’:

پایدار
pāydār
‘permanent, perpetual’

پایمال
pāymāl
‘trampled upon, suppressed, infringed, disregarded’

جایگاه
jāygāh
‘place, situation’

چای
cāy
‘black tea’

رایزن
rāyzan (also rāyzen)
‘counselor, adviser’

زایمان
zāymān (also pronounced zāyemān)
‘childbirth’

Also, there are interjections, such as آی āy ‘an expression of pain,’ also ‘ahoy!’, and وای vāy ‘an expression of surprise and astonishment,’ etc. (Also see notes in the section dealing with the Long Vowels.)

In colloquial Persian occasionally some words lose a medial vowel and a cluster with [-āy-] sound remains, namely فایده fāyde from the Perso-Arabic fāyede ‘profit,’ ‘gain,’ ‘benefit,’ ‘advantage’, آینه āyne from the Persian āyene, etc. It must be understood that technically this [-āy-] cluster is not really a diphthong.

ey is a glide very close to [-ai-] in ‘pain.’ According to dialectal variations, this diphthong may be pronounced as ay (which is historical), but not in Standard Persian. Compare and contrast Classical Persian می may ~ Modern Persian می mey ‘wine’; Classical Persian نی nay ~ Modern Persian نی ney ‘reed.’

ow is a glide very close to [-o-] in ‘close.’ According to dialectal variations, this diphthong may be pronounced as aw (which is conservative), but not in Standard Persian. Compare and contrast Classical Persian جو jaw ~ Modern Persian جو jow ‘barley’; Classical Persian نو naw ~ Modern Persian نو now ‘new.’

It should be noted that in the Tehrani dialect the [-ow-] segment is articulated without the “w”-glide, and
for compensation the [-o-] is lengthened as [-o:-]; for instance, ro:γan for r͡owγan روغن ‘oil.’ This is even the case with the loan words; such as, mo:red for m͡owred مورد (Arabic m͡awred) ‘instance, case; proper place or time, proper occasion.’

uy is a diphthong which usually occurs terminally, and primarily in Classical Persian; and in Modern Persian, it is only used in two instances: (1) in poetry (which always retains the classical features), and (2) in compound words (nouns, verbs, etc.); for instance, جویبار juybār ‘stream,’ inquirer,' رویگر ruygar ‘zinc-worker,’ ‘coppersmith,’ etc.

That is to say, in Modern Persian the /-y/ has been elided, and a variation with a terminal [-u] alone has already replaced this sound segment (namely جو ju, for the classical variation جوی juy ‘stream’). The [-uy] segment (with the retention of /y/) in compounds. (Also see notes in the section dealing with the Long Vowels.)