This is absolute bullshit. How do you take this card out when Gideon gives it flying? 1 freaking card took me out. Freaking stupid.
use cards with reach and watch the miracle happen 
Flyers with vigilance or defender will work the magic too
Your options if you’re playing red:
http://decktester.com/Cards?colors=4&abilities=14&pageSize=48&pageNo=1&sort=CardName%20ASC
You can use Haunted Cloak or True Faith Censer with any red flying creature as well.
On black languish will do it.
honestly i don’t think the party carriage is that big of a threat. it is easily removed with a bit of forethought and seeing as everyone is running it at the moment inclusion of a card or two to deal with it isn’t such a dead weight.
Really, all they need to do to fix Runaway Carriage is make it so that it loses prevent damage if it blocks a creature as well as if it gets blocked. A creature that an opponent can’t deal with and whose only option is to race it - to kill the creature’s controller before it kills them, isn’t really a problem. The problem is when said creature is also an impenetrable, indestructible wall that mows down whatever the opponent tries to put out turn after turn. And if it’s been made unblockable then there are very few cards in the game that can deal with that (nearly all of them at rare or mythic).
Around the time of the last patch, they said that they were thinking about removing the damage prevention clause entirely.
As green, play RC with Mantle of Webs and laugh at the Sphinxes, Plated Crushers, and other RC’s the AI puts on the board. Just keep a Scour primed to get rid of UC’s, Spiders, and other blockers. Or Nissa’s 2nd ability to get your toughness high enough to survive smacking a blocker.
No, it should lose prevent damage if it obtains vigilance or reach. It still has its place against berserkers, which I think was the point.
Alternatively, make hexproof weak against non-targeted support abilities. That opens up lots of ways of taking care of RC, like Blightcaster (when you cast a support, the first creature your opponent controls gains -2/-2 until the end of the turn). Currently, the effect just jumps to the first non-hexproofed creature your opponent controls.
While that should definitely be implemented against hexproofed creatures, it doesn’t solve the RC Problem. Black already has several cards that can deal with unblockable RC. Red doesn’t.
For Flying:
Colorless cards work. For 4 mana you can get a True-Faith Censer (a common), for 1 mana you can get a Haunted Cloak (a rare)(assuming you get your flying creature out first, or you play Aligned Hedron Network). 11 mana gets you a Skyraker Giant (an uncommon).
For Unblockable:
Depending on how the RC was becoming unblockable, there’s always lots of support smashing tools available to red. You can always go around the RC by using a Rogue’s Passage. Red’s creatures can hit way harder if you make your creature go around. You really don’t want to get in an arms race with a red deck.
It’s a rare, but I got it pretty early on. It’s a 1 cast cost solution to Runaway Carriage.