General sadness or longing:
* Mournfully
* Sadly
* Sorrowfully
* Despondently
* Melancholically
* Woefully
* Dejectedly
* Elegiacally
More specifically, a plaintive sound or tone:
* Wailingly
* Moaningly
* Whiningly
* Lamentably
* Grievingly
* Dirgefully
Other options:
* Longingly
* Appealingly
* Earnestly
* Pitifully
* Touchingly
The best synonym will depend on the specific context of your writing. Consider the tone and the emotions you are trying to evoke.