How to gain finger strength when playing on a keyboard?

I find that keyboard keys are far more sensitive versus a real piano's keys and it's much more difficult for me to press on a real piano as opposed to a keyboard. I have a keyboard that I practice on but when I'm expected to play on a real piano I fib a whole lot more because the keys are much heavier, but I don't have a real piano to practice on. How can I improve my finger strength so that I'm hitting the keys I need to (at allegro) with accuracy? I find that I can hit the notes on a real piano's weighted keys if I play at a slower pace such as largo, andante, or moderato but when I try to play at allegretto or something, I end up sounded like crap! Help? I really want to just find a real piano on sale to practice on but my budgets only 500 dollars):