Drops of urine continue to come out of him; what should he do in ihraam?

If the urine stops after this time, then you have to wait,
and there is no concession for you in prayer when there is najaasah
(impurity) present, because you are not regarded as suffering from
incontinence. You should choose times when there is less crowding so that
you will not disturb people with your being late. 

As for putting a piece of cloth over your private part, that
is not something that is forbidden when in ihraam. 

We asked Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on
him): What is the ruling on the muhrim (pilgrim in ihraam) who suffers from
incontinence putting something over his private part, such as a bag, so that
the najaasah will not spread? Is this one of the things that are forbidden
when in ihraam? 

He (may Allaah have mercy on him) replied: That is not one of
the things that are forbidden when in ihraam. 

And Allaah knows best.