Well I dont have a parekeet but I have a lovebird and when she was a babby I would open her cage and let her come out on her own that way she didn't feel forced and she came out and we now have a grat relatin ship and once she starts trusting you try to put him or her in youre hand and talk softly and cuddle with him or her it will make him or her love coming out and spending time with you.
-get a mini lasso and pull it out
-pretend to be another bird
-open up the cage, open the windows, and voila, freedom!
-oven mitt( this one is real, not stupid like the rest of these suggestions)
-pretend to be a mesmerizing mermaid
-pretend to be zeus and throw a fake thunderbolt at it...
-coax it with chocolate
-pour h2o on it
-squak like a parrot and the parakeet will become hypnotized and slowly fly toward u.then u catch it.
-swat it with a fly swatter and it will squak. then u dance like a tapdancing leprechaun and drink a little acohol and act drunk so ur bird will think ur crazy and zoom out of the cage cuz its so scared.
-do sum funky, hip, nifty, snazzy dance moves next to its cage. the bird will be so humiliated to be ur pet and fly out of its cage.