If you can show Return On Investment in your plan, it will make a big difference.
For example: Problem: 50% of the graduating trainees all make this mistake when reporting to their new restaurant. It costs the company “X” dollars a year. If I can have “X” dollars to change the class in training, it will reduce the mistakes by 45% and save “X” dollars over the next year. You will make your money back in the first 3 months.
Your proposed training solution should promote sales, cut costs or same time!
No creditability? Start with small training projects for small dollars. Slowly increase the size of your training projects as you gain success and credibility. Offer 3 solutions...$$$, $$ and $. They will look at it as a choice and not a Yes or No.
Also, before you formally request money for training programs, test your project plans on your peers, your boss and his/her boss and incorporate their ideas. That way everyone has seen it and knows about it when they discuss it without you.