Leyton recommended Sisko as the CO of DS9 long before the Dominion was a threat, before the wormhole was even discovered. It's unlikely Leyton was considering a coup as early as 2369.
I didn't say anything about the Dominion. I said the Cardassians. Remember, during season 6 of TNG, things weren't exactly rosy with them. Hence, my earlier post.
The Cardassians were not nearly as threatening as the Dominion. The Federation had already fought a war with them without anyone attempting a coup (presumably). The situation with the Cardassians was tense, but not that
tense. They only wanted Bajor and Minos Korva; they weren't seeking to conquer the entire Federation.
Leyton was motivated to overthrow a President he saw as weak, who wasn't treating the Dominion threat the way he thought it should be handled. I doubt Leyton was always looking for an excuse to overthrow the UFP government, though. The Dominion was a credible threat to the Federation's existence, something the Cardassians would never be. That kind of threat would drive a man to desperate measures.
At least the Dominion was an ongoing threat to justify a military junta. At their best, the Cardassians might be able to match the Federation, but not destroy them. Threats like the Borg would arise and be defeated too quickly (or, in the worst case, not defeated at all) to justify a military dictatorship of the Federation. So I think the Dominion was the first threat that the Federation encountered that could be the continual
threat that would justify Leyton's actions.