Formal:
* Sadly
* Sorrowfully
* With regret
* With a heavy heart
* Reluctantly
* With reluctance
* With apologies
* Apologetically
Informal:
* Sadly
* Unfortunately
* I'm sorry to say
* I'm afraid
* Sadly but truly
* Much to my regret
The best synonym depends on the context of the sentence. For example, "regretfully declined" might be best replaced with "reluctantly declined," while "regretfully informed" could be better expressed as "sadly informed."