Storm the Beach (This can happen at the beach island) - Individuals build a small base at the beach and everyone touching the beach is KOS to them. Attackers can use Trishna's Launchers / SBC / Crips Cannons to attempt to storm the "castle" and kill the few inside. Rewards include a very high death count, the sense of pride of wasting all your raiding materials, and perhaps a few bits of Suga.
Prop Climb - Self-explanatory. Maybe have a final fist fight to the death for those that make it in five minutes.
Race Course - Build a race course in Sitland with obstacles. First to make three laps wins. Occasional ghouls with vehicle poles can cause some mayhem.
Dodge the Bombs - Mod with SBC gets to unleash fury on the populace in Sitland. Another mod is there to teleport the victim... err, players... to Sitland to be shot over and over again. Once they opt in, they cannot opt out. There may be a point to it, but its really a ruse to have an excuse to blow up dozens of people with an SBC.
Singing Contest - Individuals try their best to impersonate T Swift in a terrible rendition of "Shake it Off". Winner gets executed by the worst singer.
Jetpack Racing - Similar to the Race Course, but it's in the air and the cost of entry is stupidly high. Death results in losing a jetpack and their pride.
Murder Mystery - This will take some effort to setup. You'd create a couple rooms and hide a few props in each as clues to the cause of someone's murder. People will have to find items which aren't physgunned and are gravgun-able. Then they'll have to put the clues together as to who the murderer is. For example, if it was Kert Kobean then you may use CDs, a shotgun, and some musical instruments. Maybe that was a poor example.
Dunk The Mod - Players take turns shooting at a Mod with HL2 Crossbows at ~100 meters away. Person that takes them out wins a Duck SWEP as a prize.