Tough situation and I feel for you.
It's tough because you want to work with the Principal in order to have his support so that you can do all of the amazing things that your group does.
At the same time you never want to set a precedence that the Principal gets whatever he/she wants whenever they want...
So, here's what I've done, which I hope you could try to apply.
First, I've created various allocations within our budget. At the beginning of the year we define what money goes in to each fund. For example, their is an allocation for music, art, gym, library, technology, etc.. If the librarian wants new accelerated reading quizes she still needs to come to us, but if she has the funds in her account it's kind of an auto. I still require them to come to the meeting because I don't want the staff members to feel they just get whatever they want, so I have them prepare an explanation/description and present it, and then we vote. I'll often say, after they do their presentation, that "there is currently x amount in the library fund, which can cover this request"...
Similarly to you situation, we have a Principal who is very into technology. It was one of his major priorities when he started a year and a half ago, and we jumped right on board. He explained, at that time, that he was slightly changing certain things, and requested that we change the computer allocation to a general technology allocation, which we did. Now, when he wishes something technology related, we look at the budget and what he has for funding from that account. If what he wants is more than what is there, but a fundraiser is going to be held that is normally used for that allocation, we will vote to allow him the purchase, but with the understanding that that allocation will be "in the red" and will need to be "paid back".
This way he can't ask for too much, and needs to still come to us.
I would say that you shouldn't give in totally. Make him come and present the need. Then refer to your yearly budget. Do you have the funds available? If you approve this will it take away from something else? Maybe you'll only be able to approve one or two this year. Maybe you can present the idea of a new fundraiser or event to fund this, and maybe try to get his/the staff's help. For example, last year the Principal wanted a brand new computer laptop cart that would have a computer for each child, which the teachers could use within the classrooms. We likes the idea, but not the $25000 price tag. We ended up fronting the money with the understanding that we would run a new golf tournament fundraiser, which the Principal actually chairing the event. It was a huge success!!!
The reason this worked was because he didn't just come to us and say, "I want it", he instead presented the idea and then said, "Here's how we can make it happen, together".
If I was you, besides defining the remainder of your year's budget, setting up certain allocations, and discussing the request at the next meeting; I would start to require all requests to be made in person. That way a staff member, in this case the Principal, will need to come to the meeting to present the idea. Questions such as how much, what's the benefits, how will this improve the instruction, etc., can all be asked. Then as President you can refer to your budget and the allocation that the request would come from, and bring it to a vote.
I hope it all works out.
PresidentJim