Since it is a supplication, one should try to perform it within a time when supplication is accepted, like the last third of the night, between the calls to prayer, and the other times in which supplication is likely to be accepted. As for supplication in the last hours of Friday, then no, because one should not supplication within prohibited times. As for standing and supplicating to Allaah, then scholars have concluded that the time for supplications being accepted is within the last hour on Friday, before dusk prayer. The person should wait for the prayer, and as long as he is waiting for the prayer, he is considered to be praying and is just like the one who is standing and praying. However, praying during this time is not permissible due to it being a prohibited time to pray.