-lWeride - you can't expect a reply in just a few minutes, you need to be patient and wait untill someone can help you anwswer your question. Posting over and over again, does not increase your chance of getting your answer that soon.
Now- to answer your question, the is no specific you make your parent leave faster. The only way is by setting your 'Tamagotchi Clock' to one minute before mid-night and waiting a minute. You can see your Paren actually saying good-bye to the baby, and leave after a fem minutes. This can only happen, though, on your second night of having the baby, and ca not happen if you pause it to long.