What isa good defence for black after the English opening (2. c4)?


After 1 c4 I play 1...c6 and try to steer the game into a version of the Slav Defense or the closely-related Caro-Kann Defense. White almost always responds with one of these three 2nd moves (and when he doesn't you can still usually get to a Slav or Caro-Kann position):
2 d4 where 2...d5 transposes to the Slav Defense where you want to move your QB to f5 or g4 before blocking it in with e6 and usually putting your QN on d7 not only prevents stable WN outposts on e5 and c5, but supports typical counter-attacks on White'center pawns.
2 Nf3 where 2...d5 is almost always followed by 3 d4, transposing into the main line of the Slav Defense.
2 e4 d5 transposes into the Caro-Kann Accelerated Panov Attack where White generally ends up with Isolated Pawns and nothing to show for it. Where the other two responses tend to end up in a semi-closed, maneuvering game, this one is often wide-open.
Possibly helpful:
Beating Unusual Openings by Richard Palliser (2006)
https://web.archive.org/web/20140627072813/http://www.chesscafe.com/text/hansen107.pdf
Grandmaster Repertoire 19 - Beating Minor Openings by Victor Mikhalevski
http://www.qualitychess.co.uk/ebooks/BeatingMinorOpenings-excerpt.pdf
http://www.davidsmerdon.com/?p=1888

I just looked at your 5 most recent bullet games. In 4 of the 5 games you moved your king out within the first few moves, sometimes even on the 2nd move (1. d4 e5 2. Kd2?). That is insanely suicidal. Do you not know how to castle? Are you maybe trying to be daring by moving your king out like that just because it is a bullet game? Such king moves are simply not done if you are trying to survive. It might help to stop playing bullet games and play normal speed games.
In comparison to the importance that problem, worrying about how to handle the English Opening is inconsequential. However, to answer your question anyway, here are the most popular responses to 1. c4:
1...Nf6 {Anglo-Indian Defense. #1 pop. 72594/230985 = 31% frequency. w 39%.}
1...e5 {"Timman Defense." #2 pop. 51875/230985 = 22% frequency. w 39%.}
1...e6 {"Flear Defense." #3 pop. 28949/230985 = 13% frequency. n 37%.}
1...c5 {Symmetrical Variation. #4 pop. 27294/230985 = 19% frequency. n 37%.}
1...g6 {"Schmidt Defense." #5 pop. 18876/230985 = 8% frequency. n 35%.}
1...c6 {"Dreev Defense." #6 pop. 15727/230985 = 7% frequency. n 38%.}
1...f5 {Anglo-Dutch Defense. #7 pop. 8389/230985 = 4% frequency. w 39%.}
Black has so many good responses to the English Opening that memorization won't help much, so here are the main ideas as I understand them:
1...Nf6 is a noncommittal waiting move to see what White will do next, and prevents White from playing e4.
1...e5 aims at an outright refutation, and is a reversed Sicilian Defense, so the result will usually be tactical. This is the best for strong, tactical players who want to win at all costs.
1...e6 is another noncommittal waiting move, and prepares to equalize with ...d5.
1...c5 signals that Black wants to draw by copying White's moves, and this can continue safely for a surprisingly large number of moves. This is probably the safest response for beginners.
1...g6 is another noncommittal waiting move for Black players who like fianchettoed defenses like the Pirc, King's Indian, or Dragon Sicilian.
Below is an example of one symmetrical variation. Warning: Black cannot safely continue the symmetry after White plays d4: Black must capture with ...cxd4 at that point, at least when there are mutual kingside fianchettos. However, Black can shortly thereafter play his own ...d5 safely, often on the very next move, and thereby equalize.