The cards can either be bought in the shop after you spend a certain amount there, or found in Dragon Universe by a character of high enough level. In DU, the cards appear at the same place for each character every time. For Goku, (probably the easiest character to get them with) they appear on an island just West-Northwest of the main continent. It doesn't matter how many times you go through DU, it is your character level that matters.

Silver Membership Card Character Lvl 2+, or spend 1,500 zenie in shop or have budokai 2 save.
Gold Membership Card Character Lvl 15+, or spend 100,000 zenie in shop.
Black Membership Card Character Lvl 30+, or spend 250,000 zenie in shop.