Note: You must see each of these rival events before you see Angelo and Daisy's equal level of rival event. Triggering Daisy/Angelo events before Dirk/Antoinette will cause an issue with triggering Dirk/Antoinette's events. There are no issues with viewing Dirk/Antoinette and then viewing Daisy/Angelo; just not the other way around.
Example: You can see Dirk/Anto black rival event, then Daisy/Angelo black rival event, then Dirk/Anto purple, Daisy/Angelo purple, etc. But, if you see a Daisy/Angelo rival event before the equal color of Dirk/Anto rival event, then you break Dirk and Antoinette's rival events and they no longer will trigger. (Source: Japanese wiki)
Black Rival Event
» Walk from Zephyr Town to the Waterfall area
» 1:00 pm to 4:00 pm - Saturday or Sunday
» Sunny, Cloudy, or Snowy weather
» Not on a Bazaar or Festival day
» Year 1, Summer 5 or later
» Antoinette (boy player) or Dirk (girl player) at a black heart color
As Dirk starts jumping up the hill, Antoinette is jumping down it. Oops! The two people almost bumped into each other, but Dirk was fast enough to move backwards just in time. He's glad to hear that Antoinette wasn't hurt.
Antoinette tells him she's fine and then quietly walks away.
Purple Rival Event
» Walk from Zephyr Town to the Hotel area
» 3:00 pm to 5:00 pm - Thursday
» Sunny, Cloudy, or Snowy weather
» Not on a Bazaar or Festival day
» You have seen the Black rival event
» Year 2, Spring 21 or later
» Antoinette (boy player) or Dirk (girl player) at a black or purple heart color
Blue Rival Event
» Zephyr Café
» 12:00 pm to 5:00 pm - Monday, Tuesday, Wednesday, or Friday
» Sunny, Cloudy, or Snowy weather
» Not on a Bazaar or Festival day
» You have seen the Purple rival event
» Year 3 or later
» Antoinette (boy player) or Dirk (girl player) at a black, purple, or blue heart color
Yellow Rival Event
» Claude's house
» 10:00 am to 12:00 pm - Monday, Tuesday, Wednesday, or Friday
» Rainy weather
» Not on a Bazaar or Festival day
» You have seen the Blue rival event
» Year 4, Summer 2 or later
» Antoinette (boy player) or Dirk (girl player) at a black, purple, blue, green, or yellow heart color