The best thing that I can tell you is to document, document, and document some more. Come up with business models that are not expensive that would provide your unit with a much needed upgrade. Sit down with management and outline why you think that the unit needs the upgrade and most important of all is to outline the benefit to the residents. Odds are you are still going to hear no the first time but the main thing is to keep trying.
To increase your budget you are going to have to get creative. Look for the areas where you can cut and then increase where needed. Show management that you can be a good steward of their money and you won't have these issues down the road.