Can a child take prescription singulair (montelukast) and over-the-counter triaminic cough and cold at the same time?

Yes: Yes he/she can. There is no conflict between those two medicines.

Depends: There is no contraindication, but cold and cough medication is not recommended under age4-6y. Therefore i would say it depends on the age of your child.

Yes: Yes, they can be taken at the same time. For children under the age of 6 years though, cough syrup is no more effective than using nasal saline to reduce post nasal drip. If your child is allergic or has asthma, the cough actually may be due to those causes and triaminic is not needed. If your child is an asthmatic, continue your asthma plan and follow up as needed with your pediatrician.

Yes: If your child is 6 or over as OTC cough syrups are not approved for younger children