* δέομαι (déomai): This verb means "I need," "I beg," or "I request." It's a relatively polite way to ask for something, implying a humble request. You'd use it in a phrase like: δέομαί σου (déomai sou) - "I beg you" (literally "I need you"). The addition of "σου" (sou) makes it more personal and polite. You could adapt this to other pronouns depending on who you're addressing.
* αἰτοῦμαι (aitoumai): This verb means "I ask" or "I request." It's a more formal and less emotionally charged way of asking than déomai.
* χαρίζεσθαι (charizesthai): This verb means "to grant," "to bestow," or "to favor." Using this in the passive voice with the imperative form ("be granted") would be a highly polite and indirect way of asking for something, almost like saying "Would you be so kind as to...?"
The best choice depends heavily on the context. There's no single word that directly translates to "please" in the way it's used in modern English. Instead, the politeness is conveyed through the verb choice and the overall tone of the sentence.