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I assume the answer is no.
I am asking, because my IME (Mozc) converts おにょみ into 音読み (same with くにょみ→訓読み).
I think this is simply a matter of convenience to save the user from having to press [n] twice, but I can't think of any other word where this kind of feature is implemented.
So is there anything more to this?
おにょみ does not make sense except as deliberate 変換ミス (e.g. for comical effect).
Handling such mistypes is a common IME feature for words with ん+ vowel combinations or ん+な行.
As shown in the screenshot, another common example is おんあ(onna)→女.
Adding on to Igor's answer, which addresses the spelling aspect. Let's look at the pronunciation.
Is おにょみ a valid pronunciation of 音読み?
In a word, no.
おんよみ is pronounced something like [[õ̞.ɰ̃.jo̞.mi]] in normal speech. This has four distinct morae ("beats", the timed length of sounds in Japanese). The ん between two vowels causes nasalization, marked by the tilde ~, with the specific mora of the ん often realized as something like a tight //u// sound with nasalization: technically, [[ɰ̃]], a nasalized voiced velar approximant.
Meanwhile, おにょみ would be pronounced as something more like [[o̞.ɲ̟ʲo̞.mi]]. This has only three distinct morae, and no nasalization.
音読み is only ever spelled in kana as おんよみ, with four kana corresponding to the four morae, and with ん correctly indicating the nasal consonant.
