For a deep sigh:
* Sigh
* Whew
* Ugh
For a yawn:
* Yawn
* Aaah
* Haa
For a tired groan:
* Groan
* Mmm
* Ugh
For a sleepy mumble:
* Mmm
* Mmph
* Mmm-hmm
Ultimately, the best way to represent the sound would be to describe it using words like "tired sigh," "sleepy groan," or "deep yawn." You could also use onomatopoeia, which is the use of words that imitate sounds.