It is often said that Japanese contains a large number of homonyms because
there was no way to render tonal Chinese words into Japanese. This makes
complete sense. But I am looking for specific examples of Sino-Japanese words
which are homonyms but where their original Chinese counterparts are not
homonyms, i.e. the Chinese words have tonal differences, but the Japanese
words do not.
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kanji homophonic-kanji chinese pitch-accent homonyms
Specific examples of tonal Chinese words rendered into Japanese
The most homophones that I know of are the various words pronounced きかん
(ordered by frequency in Japanese)

  1. 機関 _jīguān_ 機關・机关 engine/institution 
  2. 期間 _qī​jiān_ 期间 time interval/period 
  3. 器官 _qì​guān_ organ 
  4. 基幹 _jīgàn_ mainstay/nucleus 
  5. 帰還 _guīhuán_ 歸還・归还 repatriation/return 
  6. 気管 ​ _qìguǎn_ 氣管・气管 trachea 
  7. 旗艦 _qí​jiàn_ 旗舰 flagship 
  8. 季刊 _jì​kān_ quarterly (e.g. magazine) 
  9. 奇観 ​ _qíguān_ 奇觀・奇观 wonderful sight

Formatting: _kanji_ Mandarin _pīnyīn_ [traditional Chinese・]simplified Chinese
English.

In (Modern) Chinese all are pronounced differently.

In (Modern) Japanese, they can be only partly differentiated using pitch
accent. The pitch accent given in 新明解 日本語アクセント辞典 groups them as follows:

  * きかん【LHH】 ⁴基幹、⁵帰還、⁶気管、⁸季刊、⁹奇観

  * きかん【LHH】、きかん【LHL】 ⁷旗艦

  * きかん【LHL】、きかん【LHH】 ((新は きかん【HLL】)) ¹機関、²期間、³器官

Note that 94% of the occurrences of きかん (numbers from the written language)
are 機関 and 器官. For disambiguation, context is always king.
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answer
Keywords: MC, Middle Chinese; OC, Old Chinese: MJ: Middle Japanese; OJ, Old
Japanese; 呉, _Go'on_ ; 漢, _Kan'on_ ; 唐, _Tō-on_ ; /(absence of superscript)/
or 平, level tone; /X/ or 上, rising tone; /H/ or 去, departing tone; /p̚/, /t̚/,
/k̚/, or 入, entering or checked tone*

_On'yomi_ homophones are numerous, but the loss of syllable distinction comes
from multiple sources, of which loss of tones upon importation into Old -
Middle Japanese from Early / Late MC is just one. There are at least two other
major sources:

  * Phonological shifts in the Japanese language itself. If you've dabbled in [historical kana orthography](https://en.wikipedia.org/wiki/Historical_kana_orthography#Complete_tables_of_differences), you may recognise patterns when going from historical spellings to modern spellings. In fact, the historical kana spellings for many _on'yomi_ represented a more accurate mora-sequence approximation of MC syllables than modern Japanese spelling, but these written distinctions were later lost in spoken Japanese. E.g.:

    * **「協」** (呉音: _originally_ **[けふ]{kefu}** , _MC_ **/ɦep̚/** ), **「京」** (呉音: _originally_ **[きやう]{kyau}** , _MC_ **/kˠiæŋ/** ), now both reduced to **きょう**
    * **「帳」** (漢音: _originally_ **[ちやう]{tyau}** , _MC_ **/ʈɨɐŋ H/**), **「兆」** (漢音: _originally_ **[てう]{teu}** , _MC_ **/ɖˠiᴇu X/**), now both reduced to **ちょう**
  * The waves of importation of vocabulary, with readings now classified as [呉音](https://en.wikipedia.org/wiki/Go-on), [漢音](https://en.wikipedia.org/wiki/Kan-on), and [唐音](https://en.wikipedia.org/wiki/T%C5%8D-on). All of these are snapshots of both different eras of Middle Chinese phonology and different Chinese topolects during those eras. Combined with the above phonological shifts in Japanese, you can get even syllables which sounded vastly different in different topolects of Chinese in different eras (not even considering tone) converging in Japanese. E.g.

    * **「清」** (唐音: **しん** , _MC_ **/t͡sʰiᴇŋ/** ), **「森」** (呉音: _originally_ **[しむ]{simu}** , _MC_ **/ʃˠiɪm/** ), now both reduced to **しん**
    * **「生」** (呉音: _originally_ **[しやう]{syau}** , _MC_ **/ʃˠæŋ/** ), **「匠」** (漢音: _originally_ **[しやう]{syau}** , _MC_ **/d͡zɨɐŋ H/**), now both reduced to **しょう** ; for reference, the 漢音 of「生」and 呉音 of「匠」are **せい** and originally **[ざう]{zau}** , respectively.

The applicable class of words to answer this question are then those which had
syllables distinguished in MC by tone only and have merged in OJ purely due to
this loss of tone information upon importation. E.g.

  * 京 (/kˠiæŋ/, 平) vs. 敬 (/kˠiæŋH/, 去) both became [きやう]{kyau} -> きょう;
  * 真 (/t͡ɕiɪn/, 平) vs. 震 (/t͡ɕiɪnH/, 去) both became しん
  * 朝 (/ɖˠiᴇu/, 平) vs. 兆 (/ɖˠiᴇuX/, 上) both became [てう]{teu} -> ちょう;
  * 理 (/lɨX/, 上) vs. 吏 (/lɨH/, 去) both became り
  * 相 (/sɨɐŋH/, 去) vs. 想 (/sɨɐŋX/, 上) both became [さう]{sau} -> そう

* * *

*Entering/Checked tone [is not really a tone](https://en.wikipedia.org/wiki/Checked_tone).
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