For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
V Johnson
Other synonyms for earnest :
devout, heartfelt, wholehearted, sincere, impassioned, fervent, ardent, intense, urgent
"earnest prayer"
Thomas George
Earnest prayer is unchanging prayer, constant prayer in fath based on the word of God, unbreaking prayer for an answer from God.