How To Get The Most Renegades Coins

The number has always been random. You can get 1,5,10, or 25 when you pick up the item.

Did you even try the event this time?
The fossils this time give 5, 10 or 20. You know, 5+, just like Dark Link said?

Also: Once you get 1000 points worth of artifacts, you can't pick any more up that day. I've gotten 2 mystical artifacts each time I've tried (5 times so far, 2 chars yesterday, 3 today, all got 2 artifacts) so leave at least 4 days if you want the 64 Renegade coins from this event on a character.