If you do not have the room for a tree, you can plant a special plant instead. Roses and other plants with a long life make great celebratory plantings. Your child will enjoy having a special tree or plant in their name as well, and you can compare the growth of the two from year to year. Imagine having a photograph to document the way they grow and change every year.
In many cultures, burying the placenta is also a tradition. When my daughter was born, my midwife suggested we plant a tree over the placenta, so that the thing that nurtured our child until she was born would also nurture a tree as it grows. I love that idea and think it is a tradition we will take up for all of our children. You can freeze the placenta until the ground thaws if you have your baby in a cold season, as we did.
You can plant any tree or plant that has a special meaning to you, or you can plant a food-bearing plant or tree. Fruit or nut trees make great trees to plant for this occasion. Celebrating the life of your child by planting a tree that also gives life is a perfect circle.