So glad you asked this question I too find this very difficult and my Master likes to hear begging a lot. I have found he is partial to the word "Mercy".

Since we don't have the time to bring out the authentic beggar in me very often, I am training to invoke it on command. He also does not care if it is authentic, but it should appear authentic. So I mimic what I have seen, I fake it. Also, I have found that if I take a professional attitude like "begging is my job so I am gonna give it my all" has helped me get past the "I feel ____ (insert your thought here) doing this attitude" If nothing else, he is pleased by my authentic effort to try to be as real as possible, even if I am not as convincing as I think I should be.