Generally speaking, yes, they are deductible, but there are a couple of different issues here. The board should only agree to accept the donations if they fall within the scope of the organization's mission. You can't just go and have a group of parents give money to a parent group and say "use this to build a hospital," because building a hospital would have nothing to do with the mission of a parent group, and if the parent group did that, they would jeopardize their tax exemption. So this assumes that funding a playground would fall in the parent group's mission.
Also, once you start accepting this type of donation (sometimes referred to as a restricted donation), you need to make sure that the accounting is done in such a way so that those funds are kept separate and only used to fund the playground. If they playground never got built, you would have to have a way to go back and ask people if they want their playground donation back, or if they will allow you to keep it for other purposes.
If, on the other hand, donors don't put a restriction on the donation, but the board votes to set aside a certain amount of money each year to be used for the playground, then a board vote could be taken at a later date to reverse the designation. So, for example, you could just say you are going to have an auction to raise money for the parent group generally (or "for the playground and other operating expenses"). The board can decide that they want all that money to go to the playground, or a stated portion of it. Then if they change their mind, they can do that with a vote by the board instead of going back to the individual contributors.
Some people's bylaws are very specific, so you'll have to review yours and see if there is anything that would prohibit this kind of project. Most are loose enough so nothing in the bylaws would need to be changed for something like this. But, if you have a budget that has been approved for the year, and you want to make a change to that budget, your bylaws might specify how such changes must be made. For example, the bylaws might require a vote of the general membership to make any change greater than $500.