good question.
but i got myself coptic 'God parents'!
ok, i am cheating a bit, but i will tell u about them and then u will see why i call them my God parents (and also it gives an idea of what God parents should do). they were not recognised as 'God parents' in any ceremony, but they certainly do that job, and to call them 'my friends' doesn't seem to be a good enough description.
they are the people that said to my husband and i (before i was orthodox) when we visited their house that we were just as welcome as their own children and then they acted like God parents by inviting us often for lovely food and having many beautiful conversations full of love and really good spiritual advice.
it is there i learnt how to enjoy CTV (spiritual channel full of liturgies and poems and spiritual advice) and how to make really good biscuits. there i saw how God's love jumps over language and culture barriers, and there i saw how people who are close to God can stay strong and faithful despite the traumas of life (illness, pain, family bereavements etc.)
my 'God brother' helped us move house once and another 'God brother' gave useful advice many times. it is my 'God sister' who i contact everytime it's my anniversary of becoming orthodox and who cheers me up with her sweet smile and impresses me with her kindness always. my God mother who shows me how to stay humble while being full of God's love. she also taught me the most important ingredient in the kitchen; lots and lots of prayer! my God father explains everything to me and answers my non stop questions with amazing patience. sometimes he has fallen nearly asleep with my questions, but never complained!
ok, i realise this may not have helped; as i don't know who can live up to these examples! but if you try, you will be a great God parent.

ps: found a link for mor ephrem:
http://www.copticheritage.org/rites/26_the_sacrament_of_holy_baptism