IMO Trotsky always had the worst prospects--unless we have a *really* early POD, well before Lenin's strokes. (E.g., avoid the 1920-21 "trade union controversy" with Lenin, which got Trosky's ally Krestinsky removed as the Party's "Responsible Secretary.") If in 1923, Trotsky had pressed the issue of Lenin's "Testament" he *might* have gotten Stalin removed as General Secretary, but even if he did, the likely beneficiaries would be Zinoviev and Kamenev, not himself.
As for the idea of a Trotskyist military coup, I'll quote an old soc.history.what-if post of mine:
***
The question has sometimes been raised...whether Trotsky could have used
his positions as commissar of war and chairman of the Military
Revolutionary Council to launch a successful military coup against his
factional opponents during the 1920's. The Zinoviev-Kamenev-Stalin
triumvirate very likely had some fears on this score in the mid-1920's; as
early as January 1924 they removed Trotsky's ally Vladimir Antonov-
Ovseyenko as head of the Political Directorate of the Red Army and
replaced him with Andrei Bubnov. (Bubnov had also been a Trotsky
follower--he had signed the "Declaration of the Forty-Six" though with
some reservations [2]--but had gone over to the triumvirate's side.)
Trotsky was to write in 1935 that a military coup would have been easy--
indeed he makes it sound *incredibly* easy--but that he had rejected it
for principled reasons:
"There is no doubt that it would have been possible to carry out a
military coup d'état against the faction of Zinoviev, Kamenev, Stalin,
etc., *without any difficulty and without even the shedding of any blood*;
but the result of such a coup d'état would have been to accelerate the
rhythm of this very bureaucratization and Bonapartism against which the
Left Opposition had engaged in struggle." [my emphasis--DT]
http://www.marxists.org/archive/trotsky/1935/11/stalin.htm
Likewise, Victor Serge--who retained his admiration of Trotsky even after
breaking with him politically--in his *Memoirs of Revolutionary* (pp.
234-5) wrote that Trotsky could easily have defeated his opponents by
relying on the Red Army:
"...[A] coup against the Politbureau of Zinoviev, Kamenev, and Stalin
would have been possible, and in our Oppositional circles we had weighed
this possibility. The army and even the G.P.U. would have plumped for
Trotsky if he had wished; he was always being told this. I do not know if
there were any formal deliberations on this subject among the leaders of
the Left Opposition, but I do know that the question was discussed (end of
1925, beginning of 1926) and it was then that Trotsky deliberately refused
power, out of respect for an unwritten law that forbade any recourse to
military mutiny within a Socialist regime; for it was all too likely that
power won in this way, even with the noblest intentions, would eventually
finish in a military and police dictatorship, which was anti-Socialist by
definition."
http://books.google.com/books?id=zgqahLS2NFwC&pg=PA234
Serge goes on to quote the 1935 Trotsky statement cited above (with a very
slightly different translation), and adds:
"Rarely has it been made more sharply obvious that the end, far from
justifying the means, commands it own means, and that for the
establishment of a Socialist democracy the old means of armed violence are
inappropriate."
http://books.google.com/books?id=zgqahLS2NFwC&pg=PA235
Before we accept this portrait of Trotsky--out of principled opposition to
bureaucratization and Bonapartism, nobly sacrificing a chance to come to
power--we should ask whether a military coup would have been that easy, or
indeed even possible. Here I would tend to agree with Roy Medvedev, *Let
History Judge: The Origins and Consequences of Stalinism* (1989), pp.
133-136:
"... The idea of a military solution to the internal party conflict
occurred to some members of the Trotskyist opposition. Zinoviev, Kamenev,
and Stalin had some apprehensions in this regard, which explains the
changes made on the Revolutionary Military Council as early as 1924 and
the removal of Antonov-Ovseyenko as head of the Political Directorate of
the Red Army and his replacement by Bubnov.
"It must be said quite emphatically, however, that at the time of the
discussion in the party there was never any real threat of a military
coup, if only because the Red Army was never just a 'docile' instrument in
Trotsky's hands. Trotsky could rely fully on the soldiers of the Red Army
when he gave the order to march on Warsaw, but he could not have raised
the Red Army against the Central Committee and the Politburo...
"If Trotsky in 1924 thought as he wrote in 1925, it would have been one
more of his illusions... [A] military ouster of the triumvirate and the
party apparatus loyal to it would have been an extremely difficult and
uncertain undertaking--an adventure with very little chance of success. If
Trotsky refrained from such a step, one can assume that what held him back
was not concern over Bonapartism but uncertainty of his control over the
Red Army.
"The German edition of Serge's memoirs contains a foreword by the
prominent German revolutionary Wollenberg, who went to live in the Soviet
Union after the failure of the German revolution and in the thirties fled
to the West from the persecution of the NKVD and the Gestapo. Wollenberg
convincingly disputes the version of events presented by Serge:
"'What a colossal mistake in assessing the concrete situation that had
arisen in the land of the Soviets within a few months after Lenin's death!
I must add that at the time Lenin died I was still on military duty in
Germany. As a specialist in civil war I held a prominent post in the
German Communist Party. At that time I thought along more or less the
same lines as Serge and as Trotsky apparently thought about all these
matters for another decade or more.
"'But when I moved to Moscow, I saw my error. In Moscow I was forced to
realize that the leading figures on the Red Army general staff, such as
Tukhachevsky, with whom I became friends, admired Trotsky greatly as the
organizer of the Red Army, as a man and a revolutionary, but at the same
time they took a critical attitude toward his general political position.
"'...I had very close contact with the army in general, and, through it,
with the Russian village. There could be no doubt that the top military
command had full confidence in the party leadership.... And in the entire
party there was an unquestionable majority in favor of the triumvirate,
that is, the leading threesome formed after Lenin's death: Zinoviev,
Kamenev, and Stalin. That was the order in which the importance of the
three members was estimated at the time--with Stalin last.
"'If the Soviet constitution could have been changed for a plebiscite to
be held, it is impossible to say which of Lenin's successors would have
gathered the most votes. But it can be said for certain that, given the
hostility of the peasants and the middle class (which was reappearing in
the first half of the 1920s) in relation to Trotsky, who was considered an
'enemy of NEP,' the outcome would have been rather unfavorable for him.
"'It is necessary to state this with full clarity because to this day
Trotskyists of all varieties, as well as Soviet experts in West Germany
and other countries, continue to spread the tale in speech, in print, on
radio and on television that after Lenin's death Trotsky supposedly missed
a 'sure bet.' Apparently Victor Serge believed this too right up to his
death.'"
http://books.google.com/books?id=91fB88t2_zwC&pg=PA133
https://groups.google.com/d/msg/soc.history.what-if/EAA2ui89o8I/SINb3uPQ9sUJ
***
The best prospects IMO were those of the "Rightists." In 1928, they had three of the nine full members of the Politburo, the editorship of *Pravda* (Bukharin), the head of the Government (Rykov), control of the trade unions (Tomsky), and control of the Moscow Party organization, the most powerful in the country (Uglanov). All it would take would be a couple of waverers to join Bukharin, Rykov and Tomsky in 1928 to make a Politburo majority. Kalinin was supposed to have Rightist sympathies, and Voroshilov, despite being Stalin's crony, had to have some concern about the effects of radical anti-peasant measures on a mostly-peasant Red Army.