The tzedakah doesn't have to be money. In the winter months, collect children's gloves and mittens for needy families. In the summer, ask guests to bring school supplies for children who cannot afford them in September. Not only will this put smiles on the faces of needy kids, but it will also clean out your shelves and closets. Don't forego all gifts entirely.
Children deserve something special on their birthdays.
Don't worry about what the other parents will think. Do what's right for your family and your child. Don't force your child to do something just because you say so. Introducing tzedakah concepts is tough. If your family is not actively involved in charitable giving, you will need to start slowly and build up to a major project like a tzedakah birthday party.