I could see the Reichswehr doing a military coup if the KPD reaches a majority or gets very close to one in the Reichstag elections. Between the last two German elections pre-Machtergreifung, the NSDAP's share of the vote declined while the KPD and the DNVP gained more support. It could probably look like Chile under Pinchet or Argentina during the Dirty Wars, with a conflict between a right-wing military junta and leftist parties.
It would have been difficult for the KPD to get an actual majority, or close to one, in the Weimar system - proportional representation tends to prevent single-party majorities unless you throw in something like the 50 "bonus seats" in Greece for the first-place party, or a high cutoff for entering parliament. The Nazis came closest with their 43.9% in March 1933. However, would an SPD-KPD coalition with cabinet seats for the KPD (which I suspect is the closest they'd have gotten) been enough to prompt a coup attempt?
I don't know a whole lot about the smaller parties in the Weimar Republic, but if you look at the large parties as broadly pro- or anti-Weimar Republic, here's the breakdown from the last five elections. So if at least some of the ones I'm not sure about were willing to support the Republic, then 1930 was the last election where a pro-Weimar, anti-Nazi coalition could have been formed without the support of the Communists.
1928
Pro-republic 301 (SPD 153, Centre 61, People's Party 45, State Party 25, BVP 17)
Anti-republic 139 (DNVP 73*, Communists 54, Nazis 12)
Not sure 51
(The DNVP was actually more moderate under the leader they had in this election, however.)
1930
Pro-republic 280 (SPD 143, Centre 68, People's Party 30, State Party 20, BVP 19)
Anti-republic 225 (Nazis 107, Communists 77, DNVP 41)
Not sure 72
July 1932
Pro-republic 241 (SPD 133, Centre 75, BVP 22, People's Party 7, State Party 4)
Anti-republic 356 (Nazis 230, Communists 89, DNVP 37)
Not sure 11
November 1932
Pro-republic 224 (SPD 121, Centre 70, BVP 20, People's Party 11, State Party 2)
Anti-republic 347 (Nazis 196, Communists 100, DNVP 51)
Not sure 13
March 1933
Pro-republic 219 (SPD 120, Centre 73, BVP 19, State Party 5, People's Party 2)
Anti-republic 421 (Nazis 288, Communists 81, DNVP 52)
Not sure 7