Donations received are income.
Once the income is recorded, it can be deposited to a bank account for that funding requirement. Some folks use separate bank accounts per fund, which works well. Others use a sub account in QB of the fund bank account to record the deposit for that fund.
If you use the sub bank account concept, remember that you do not post any deposit or withdrawal to the parent account, every transaction is posted in the sub account.
In order to post to a liability account, there would have to be an offsetting expense or deposit. Since income creates a deposit you can not use that twice.