That's definitely going to be a tough one as those areas fetch a pretty penny. If you are willing to live south of the park, you can find a 1 bedroom in Kensington or Ditmas Park in your price range. These neighborhoods are up and coming as many people being priced out of the more expensive areas north of the park are now migrating there. I'd be happy to assist you in your search.
The only one I could find on Trulia I linked below.