Formal:
* Pleadingly: This emphasizes a sense of urgency and desperation.
* Supplicatingly: This suggests a more humble and submissive tone.
* Beseechingly: This implies a strong desire for something and a willingness to do anything to obtain it.
Informal:
* Beggingly: This is a more casual and direct way to say "imploringly."
* Earnestly: This emphasizes sincerity and conviction.
* Desperately: This implies a sense of urgency and hopelessness.
Other Options:
* With a plea: This is a more literal way to describe an imploring tone.
* In a pleading voice: This describes the actual sound of the voice.
The best synonym for "imploringly" will depend on the specific context and the speaker's intent.