To ask earnestly is to make a sincere and heartfelt request. However, there are various synonyms for this phrase that are equally effective in communicating a deep desire for something. For instance, one could plead, implore, beseech, beg, entreat, supplicate, appeal, petition, or solicit their request. These words denote a level of urgency and importance in what is being asked. They show that the speaker is not just asking casually, but rather with a sense of seriousness and desperation. Being able to communicate one's request with the appropriate level of urgency can often be the difference between getting what you need and going without.