Can I use Sableye's "Bewitching Eyes" attack to copy my opponent's "Archie's Ace in the Hole" or "Maxie's Hidden Ball Trick" supporter?
Yes you can, as long as you meet the requirement of having no cards in your hand when doing so.
Source: TPCi Rules Team (2015-09-17)

Relevant cards

Note: All applicable cards may not be listed below.
XY7_44