It depends on the time controls. In bullet, most certainly Road Runner. In OTB Wile Coyote would get tricky, positional and chew every bit of Road Runner's position :)
if Wile C plays chess with Road runner who would win

-- wow I never expected an answer as smart and clever as yours - your answer is neat - I must make a note to never get into a battle of wit with you
How about getting into a battle of chess?

I don't know, but since Wiley and Road Runner were on TV over 50 years ago I can definitely say the following with 100% certainty:
Since Wiley and Road Runner are not up on current opening theory and are not cognizant of modern chess strategies and principles, any current player (even drunk or on a bad acid trip) rated over 2000 could crush them in a 20 game match.
if Wile Coyote played a game of Chess with the Road Runner who would you bet on to win ?