Businesses have three reasons to do things: increase revenue, cut costs, and reduce risks. (I've seen this various places, Bob Lewis comes to mind.) To make a business case for doing something, you need to show how your proposal will impact at least one of these three.
The wording of the question eliminates increasing revenue. That said some of what you said indicates that your ideas might produce revenue, but it's not likely to happen immediately. For example, if you create a useful Drupal module, this could create exposure for your company which could bring in new business.
Without using the increased revenue option, your best bet is probably to "sell" your idea as a cost cutter. Is it something that can eliminate labor? Will it speed up a slow process? Can it be re-used?
Showing that your idea would reduce risk can be problematic. It is often difficult to show what risks are present, what the probability is that something bad will actually happen, and what the costs would be if something bad does happen. However, if you can make the case that the losses would be crippling, the probability high, or the costs low, you may be able to convince management that the work is worthwhile.
Of course, if you can make a legitimate case that two or all three of these factors would be positively affected by your proposal, you increase your chances of approval.