My 1 year old had a cold 7 weeks ago but still has a persistent cough, especially at night.

Persistent cough!: There are many types of cough that can persist after a cold. If it is worse at night it could be due to post nasal drainage which could indicate an allergy. Is it a wheezy cough? If so it could suggest bronchospasm. Is it a wet cough? This could suggest a secondary pneumonia particularly if associated with fever. You should see a good pediatrician to check it out.

Post viral: After a viral illness, the airway may be more prone to bronchospasm which results in prolonged cough. A bronchodilator may be indicated, and a visit with your pediatrician is indicated. Monitor for fever, rest and provide fluids.