I do not think the "Leningrad Opposition" in 1925 could oust Stalin, even with Dierzysnki's support. The Central Committee by then had been packed with Stalin loyalists; Zinoviev's control of the Leningrad organization was simply no match for the Stalinists' control of most other party organizations (above all in Moscow, where Uglanov was First Secretary). Moreover, Zinoviev was not well-liked, and while he drew distinguished supporters like Kamenev, Krupskaya, and Sokolnikov, the latter two had little real power. (There was also the point that Zinoviev, who had been violently critical of Trotsky in 1924, looked like a hypocrite in taking "left-wing" positions on world revolution and NEP in 1925 which resembled Trotsky's--even before the two reached a formal alliance in 1926.)
So long as party control was determined by "legal" means, then, Stalin had the advantage. As for a coup, in the first place Dzierzynski was already in poor health, but even if he were healthier, I don't think the GPU could accomplish a coup by itself without the Army's support. And the latter was unlikely--even if we assume Frunze would have supported such a coup (which I doubt), Frunze too was in poor health, and would have been in no condition to assist a coup even before his ill-fated surgery:
"An additional source of anxiety was Frunze’s fragile health. Despite an operation in 1916 for a perforated ulcer, he continued to endure chronic inflammation, and doctors had warned him his internal organs were utterly frayed, counseling a surgical excision, the only known treatment at the time, but he would only agree to less invasive treatments. Thus it went for years until summer 1925, when his internal bleeding worsened considerably; in early September, the politburo mandated a seven-week holiday. Frunze left for Yalta with his wife, Sofia, but on September 29 he returned to enter the Kremlin hospital. No fewer than twelve leading internists and surgeons examined him in two rounds, concurring on the need for surgery.297 “I now feel completely healthy and it’s laughable even to contemplate, let alone undergo an operation,” Frunze wrote to Sofia, still in Crimea, on October 26. “Nevertheless, both sets of consultations decided to do it. I’m personally satisfied with this decision. Let them once and for all make out what’s there and try to establish a genuine treatment.”298 Two days later, he was transferred to the country’s best facility, Soldatyonkov Hospital, where Lenin had been operated on, and the next afternoon a team led by Dr. V. N. Rozanov, who had treated Lenin, performed an operation. A day and a half later, in the wee hours of October 31, 1925, Frunze died of what the newspaper reported to be heart failure provoked by anesthesia.299 It seems he had been administered a heavy dose of chloroform, which might have provoked dystrophy in the muscles of his vital organs.300 Frunze was buried near the Kremlin Wall on November 3.301 Pishpek, Kyrgyzia, where he had grown up, was renamed for him.
"Rumors were instigated that Trotsky’s people had killed the proletarian commander in revenge for taking his place, while Trotsky’s acolytes turned the tables, accusing Stalin.302 Beyond these false accusations, Bolshevik susceptibility to illnesses became the talk of the day as a psychoneurologist presented a grim report about pervasive “revolutionary exhaustion and attrition.”303 Nearly half of all visits by top party figures to medical clinics were for nervous disorders (with tuberculosis well behind, at around one quarter).304 Two German specialists were imported to examine a list of fifty regime figures, beginning with Dzierzynski and Mezynski and working through to Rykov and Stalin, with what results remains unknown, but the internal discussions indicate acceptance, including by Trotsky, of the fact that Frunze had died of natural causes, even if better medical care might have saved him.305 For Stalin, Frunze’s demise presented yet another opportunity [to apppoint Voroshilov]..."
https://books.google.com/books?id=wLvaCwAAQBAJ&pg=PA575