Many languages have diphthongs that end in [j], [w], [ɪ̯], [ʊ̯], and [ə̯], and sometimes diphthongs will end in [e̯] or [o̯], but besides Hmong's [aɨ̯], German's [ɔʏ̯], and all the weird diphthongs that some English dialects have going on (like [əʉ̯], [ɘʏ̯], [æɔ̯], etc.), what languages have diphthongs that end in other vowels, and why are diphthongs like [aɥ] and [aɰ] so uncommon in languages that have [y] and [ɯ]?
Supposing a diphthong not to be a special kind of phoneme, but rather just a combination of a vowel phoneme and a glide phoneme, then if a glide phoneme is uncommon among the languages of the world, so should the corresponding glide part of a phoneme be uncommon. In your question, you mystify us by writing the glide parts of diphthongs as if they were vowels.
The term "diphthong" is much abused and undefined. The main issue is precisely whether the two elements are "vowels", or might one be a glide. Your transcriptions presuppose that one of the elements is non-syllabic (noting the diacritic), i.e. not a vowel but rather a glide. A requirement of being a "diphthong" is being a sequence within one syllable, so [ai] could be a diphthong, but [a.i] could not. These are matters of phonological analysis, not phonetic observation, so you can't determine whether a sequence of two vocoids is monosyllabic vs. bisyllabic, or ends in a vowel vs. glide, just by listening. Some apparent German examples such as [fiɐ̯] "four" are not examples, if you analyze this as the phonetic realization of coda r. Also note that there is a well-establish distinction between "rising diphthong" and "falling dipthong". Rising diphthongs would end in a vocoid of greater sonority, such as [a, e, o]. North Saami has only rising diphthongs, ending just on those vowels.
It appears that the "other vowels" that you're interested in are vocoids other than [j w ɪ̯ ʊ̯ ə̯ e̯ o̯], which means [y ɯ ø ɛ æ œ ɔ ʌ a ɑ...] well I'm not gonna write them all out. So... Norwegian has [øy] ('island') and [æʉ]; Finnish has [yø] 'night' as well as [ey, æy]. Rising diphthongs that end with [a] are not particularly remarkable, existing in Saami languages as well as Faroese and Romanian.
A hallmark, perhaps a defining feature, of diphthongs is that they are a proper subset of the possible monosyllabic vocoid combinations. While Norwegian has [øy], it doesn't have [iy, oy, ay]. I don't know what the evidence is that [ay, aɯ] are very uncommon, at least given the background of general diphthong uncommonness. But I suspect that if it could be shown that they are uncommon, then that would be the product of the uncommonness of [y ɯ] times the uncommonness of diphthongs that don't simply all end in [i u]. Given the facts of intrinsic duration, a bivocalic sequence ending in a non-high vocoid is likely to have a greater duration on the second part, which would encourage a bisyllabic analysis (ergo not a diphthong).