Babies that are 6 month old can be fed with rice or congee containing bird's nest.
Just don't expect too much from it that your child will cough a lot less with bird's nest. Try try is OK, and watch out for allergic response, that should be uncommon.
I had asked this question to the people I used to buy bird nest before. He said don't give to baby before 1 yrs old. Even after 1 yrs old, once a week with one tea spoon is OK. Now, my boy is 2 yrs old. I give him one table spoon twice a week. Bird nest cannot help coughing much. For coughing, U may try 喉祖散.