From 20 minutes onwards when not in combat. (Also at game start but that doesn't really count.)
I wouldn't describe them as gold coins but I suppose they could be, but you're probably describing bounties yes. see http://leagueoflegends.wikia.com/wiki/Kill#Bounties
Super minions spawn every 30 seconds in a lane when an inhibitor is down (2x if all 3 are down). Inhibitors respawn after 5 minutes so 10 supers per downed inhib. In the unlikely event all 3 inhibs are downed simultaneously so you get a full 5 minutes of 2x supers that'd be 60 supers over the course of 5 minutes.
For the first 20 minutes, 1 Siege minion is spawned every three minion waves between the melee and caster minions. After 20 minutes, Siege minions spawn once every 2 waves and from the 35th minute onward, Siege minions spawn every wave to accelerate the game pace by making pushing easier. (They won't spawn if supers are already spawning in that lane.)