Emphasis on the intensity of the plea:
* Earnestly: She pleaded earnestly for her friend's release.
* Fervently: He pleaded fervently for forgiveness.
* Passionately: They pleaded passionately for justice.
* Desperately: He pleaded desperately for help.
* Vehemently: She pleaded vehemently against the proposed law.
Emphasis on the manner of the plea:
* Tearfully: She pleaded tearfully for her lost dog.
* Humbly: He pleaded humbly for a second chance.
* Politely: They pleaded politely for a refund.
* Loudly: He pleaded loudly for attention.
* Silently: She pleaded silently with her eyes.
Emphasis on the time of the plea:
* Repeatedly: She pleaded repeatedly for her case to be heard.
* Continuously: He pleaded continuously for mercy.
Other relevant adverbs:
* Effectively: She pleaded effectively with the judge.
* In vain: He pleaded in vain for understanding.
* Successfully: They pleaded successfully for a new trial.
The best adverb to use will depend on the specific context and the desired effect.