This is a fine place for us to try and assist you and BTW, welcome to FlyerTalk.
I actually think that GoingAway gave you some nice direction. For what you are looking for, it is best to assume that the main offices of these airlines and hotel companies are just not prepared for this type of donation process – because it is simply too popular a request.
As noted, the best approach is to contact, usually in person, the general manager of some of your leading local hotels. Often owned by franchisees, they can make a decision that requires no forward paperwork. Now, that's the hotel side of things. As for airlines, a little trickier. My general advice here is that sometimes, though not common, you can contact the "city manager" of a particular airline in your area and they can direct some information on their local policies for contributions to these types of things. The most successful things I've seen is when organizers like yourself, tap into the vast number of "friends of flyers" that know of frequent flyers who you can appeal to for a donation of an "award" to a destination or open destination. Oftentimes, it is best to try and match the free ticket/mileage award, with another donation and try to auction off the package for your fundraising. For instance, maybe the local general manager of a hotel in your area can give away two weekend nights at another property that the franchise owns. Pair that up with the free ticket and you've got an attractive offer for people to bid on. Now, airlines do have rules that prohibit "bartering" and thus it may seem like this is against those policies. But, airlines are fully aware that in situations like this the frequent flyer is simply donating to a cause and that nothing really is being bartered. If you choose this path, make sure that it is understood that frequent flyer miles are part of the package and that the winner must be flexible for the dates of travel they might consider - trust me, in the fundraisers I've been a part of that "joke" will get plenty of laughs but will not deter people from bidding on it.
Whatever your course, it is important that you plan in advance of your pitch, the specific benefits the donor can get from this. Charity is nice, but making sure you are giving prominent exposure to the hotel company, the person donating and even the frequent flyer is a real show of class. Think in advance what you can do to promote their participation. As well, think of other fun things besides free room nights. The hotel might have a nice restaurant, a party room for someone's birthday or other event for up to 15 people with choice of appetizers, etc.
As for airlines, maybe not a free ticket, but honestly, try asking for a packet of free airport lounge certificates (I'd bid on that).
Hope all this helps and in the spirit of FlyerTalk, would invite others to offer up their advice as well.
Again, welcome to FlyerTalk and always feel comfortable asking us questions.
Randy