Here are the current worst teams by record in MLB and their best pitchers:
MN- No SP'ers with an ERA under 5.00, except Pat Dean who has a WHIP over 1.41. The only 2 RP'ers having decent years are 30 year old Fernando Abad and 31 year old Brandon Kintzler.
ATL- 25 year old Julio Teheran as been discussed (2.93/0.989), but there's also 23 y/o Matt Wisler (4.23/1.181) and 25 y/o closer Arodys Vizcaino (2.22/1.235 but with a 13 K/9 rate). There's also lefty RP'er (26 y/o) Hunter Cervenka (3.10/1.180 and 12.0 k/9)
SP- Tyson Ross is hurt, but there is lefty 27 y/o Drew Pomeranz (2.88/1.173 and 10.7 K/9) and 39 y/o closer Fernando Rodney who has yet to allow an earned run in 23.1 IP (0.857 WHIP/ 8.1 k/9). 29 y/o lefty Ryan Buchter is off to a nice start (1.86
CIN- Dan Straily (27) 3.66/1.195, Brandon Finnegan (23 lefty) 3.61/1.312
OAK- Sonny Gray has been hurt and not pitching well, 36 y/o Rich Hill is on the DL, but they have quite a few RP'ers doing well so far this year. BB has a history of trading RP'ers often: Ryan Dull (26) 2.31/0.800, Sean Doolittle (29 lefty) 2.67/0.926, Fernando Rodriquez (32) 2.65/0.971
AZ- I doubt Greinke is even up for discussion, so all that's left are 4 RP'ers: Tyler Clippard (31) 3.65/1.378 and 10.2 K/9, Daniel Hudson (29) 1.73/0.846, Jake Barrett (24) 2.16/1.040 & Brad Ziegler (36) 2.93/1.446.
LAA- I don't see anyone worthwhile that is healthy and doing well, except RP'er Cam Bedrosian (24) 1.61/1.299 and 9.7 K/9.
PHI- 23 y/o Aaron Nola 3.51/1.134/9.9 K/9 and Jerad Eickhoff (25) 3.40/1.172 are doing very well. Vincent Velasquez (24) is on the DL 3.65/1.265 and maybe a couple RPers Hector Neris 11 K/9 and David Hernandez 11.5 K/9.
MIL- Zach Davies (23) 3.88/1.181, Junior Guerra (31)3.81/1.178 & Jimmy Nelson (27) 3.92/1.353 plus RP'er Tyler Thornburg (27) 2.60/0.759 and 12.7 K/9 rate.
I haven't even heard of some of these guys, and I'm no expert on other teams' players, but maybe someone from this group can become available and eventually help us.