Use the noun adjuration to describe the serious, whole-hearted way you begged your parents to let you have a puppy when you were little.
During your adjuration to get that puppy, did you say, "I swear I'll feed it and walk it every day! I swear to clean up after it!"? If so, you were really in tune with the origin of adjuration, the Latin ad- or "to" and jurare, "swear" — in the sense of taking an oath of honesty. Adjuration involves both begging and promising.