What if you did a whole family home evening centered on the birthday child?  You can talk about his/her birth, everyone can contribute to fun stories or funny sayings that they remember.  Then as a lesson, give an example how that child is like Jesus. You can choose a principle and liken an example of that child to Christ.  I bet your child would be beaming with happiness to know that you recognized his good efforts and to liken him to the Savior.   In my family we had the tradition of waking up to everyone singing Happy Birthday from the family and breakfast in bed.  We got to pick the meals that day and slept on the birthday pillow! (It was a pillowcase you slept on once a year that had birthday fabric, we did this for Christmas season too).

ADDITIONAL IDEAS:

Let each family member say something special about him/her.
Create a scrapbook page
Choose the child's favorite dessert for the treat or have birthday cake
Make a time capsule together
Look at child's photo album / scrapbook together
Read their favorite scripture stories