You could have a smooth day or wish that the day run smoothly ,but that is not the commonly used expression in this case. Usually you would be saying : 'have a good day' It seems you are literally translating from Spanish ! (Que te sea leve ) !

We just say, "Have a good day" or "Take it easy."

No, you can't say 'a smooth day'. That doesn't make sense in English. Things can run smoothly or go smoothly, but here 'smoothly' qualifies the verb, and it cannot refer to the day itself. If someone has a potentially difficult day ahead, you might say something like 'I hope it all goes smoothly today' or 'I hope it all goes well today'.