I just went through this with my daughters. Are you doing printed invitations? If you look at what true etiquette would be - you cannot ask people NOT to bring gifts. However, in this day & age, lots of people do ask on invitations for NO GIFTS. There are other, more creative or cutesy ways to say it, other than the traditional "no gifts, please." ... You can say, "no gifts, thank you", which is still simple, but somehow sounds nicer, I think. You can also say something like, "Your presence is your present." or "Your presence is your gift." We ended up saying "No gifts, thank you. (Your presence is your present!)" ... Through all of this, you can mention to those close to you that you are serious about not wanting gifts, but you cannot be upset when people bring them anyway. And if they do, don't put them out on display or open them in front of everyone - just say thank you and bring them to another room. One other suggestion I've seen is to request that in lieu of gifts, the guests bring a nice inspirational poem/writing or photos for a memory book.
All this being said, if you look at etiquette guides (and frankly, what seems like the "right thing to do"), you CANNOT ask people for a DIFFERENT gift (a.k.a. the TV). The one exception may be as an informal discussion with really close family/friends (grandparents, etc.) regarding what your daughter really wants. But I think it would be pretty tacky to be approached about this topic or to receive a printed invitation with the request for a contribution to a TV Fund.
I don't mean to sound judgemental, but I'm trying to tell you how it sounds as someone invited to such an event. Not only would I interpret it as tacky, but I might be annoyed that you just put me in a really difficult position. Do I contribute to a TV Fund & disregard the fact that it doesn't seem to go along with a religious event AND totally goes against my better judgment (I wouldn't put a TV in my kids' room!!)? Or do I do what I feel is right, buy your daughter something else, and know that you and she will both be disappointed, no matter the gift.
If it were me, I would simply ask people for no gifts, knowing she will get some anyway, and might have to return some. Knowing that I wouldn't want to put even ONE person in that predicament I described above, I would avoid the request for contributions to the TV fund.