As a participant in the previous dialog on this matter, let me just say that there is little agreement on the topic. So, here are a few things to ponder:
1) Some saints advocate saying the Jesus Prayer during services, but this seems to be a means of focussing the mind as opposed to an alternative service.
2) We use the Jesus prayer to focus the mind on God rather than a means of escapism (i.e. "I need to stop thinking and start paying attention, so I will say the prayer until I am back in reality again" versus "I don't like this hymn or the sermon, so I will find a 'happy place' rather than be uncomfortable or challenged").
3) Wearing the rope in public can be interpreted as a means of demonstrating one's 'piety' like the Pharisees who prayed on the street corner.
4) Having a rope openly may also engender questions and lead to opportunities for evangelism.
5) A prayer rope should never be a rear-view mirror ornament! A cross is more appropriate.
6) "To the pure all things are pure." If you wear the rope to impress others or convince yourself you are a Christian, then it is a sin. If you wear it because you need it because you are weak, then wear it.
7) I carry mine in my pocket, and I make sure not to let it be seen. It is intimate for me.
8 ) Depending on your level of development, the Jesus Prayer serve different purposes. In the beginning, it is a means of avoiding sinful thoughts. Then, it becomes a means of focussing on God. Then, it becomes the only appropriate thing to say. Most of us never get to the third level. We do need to know why we have it and what we are using it for. Sometimes we need to pay attention to the road and to God, and other times to God alone. Know the difference.
9) Sometimes you may need to not wear the rope depending on others around you, just as you would not wear a swimsuit to a funeral. If you are determined to go to that "Black Sabbath" concert, please don't bring your prayer rope (though you will certainly need it afterwards)!
10) You can also carry beads in place of a rope. I made mine from date pits. On Mt. Athos, some of the monks make then from seeds of a tree they call the 'Tears of the Theotokos.'
11) Take care of your prayer rope like you would an icon. It is holy.
Anyway, that's my 2¢.