Estonia v. Haiti... are these the only two powers involved, or can I involve more? If the latter...
Estonia, in an effort to increase its presence on the world stage, commits most of its military to the US-led Operation Uphold Democracy under the authority of UN Resolution 940 - troops that are needed since a sizable portion of the US military is committed to UN operations in Somalia, Rwanda, North Korea and Yugoslavia. (Not that there won't be US troops available, just less than there were in OTL). The Estonians, alongside Polish, American, and Argentine troops, successfully defeat the Haitian military government; Estonia suffers 40 casualties during the fighting.
If the former...
Estonia - the union of the governates of Esthonia and Livonia - gained independence in 1858, amidst the collapse of Russia in the Crimean War. Estonian investors contributed significant funds to various projects of the Geffard regime in Haiti; when this regime was overthrown by Sylvane Salnave in 1867, Estonia attempted to 'recoup on its investment' by deploying gunboats and troops to Haiti, ostensibly to support the "legitimate" government of Geffard. Salnave's troops handily defeated the Estonian/Geffardite invasion in Artibonite; the American ambassador to Estonia convinced the Estonians to back down, recognize Salnave, and forget any imperial ambitions.
Odds are that butterflies of a nasty Russian collapse (to the point that the Baltic governates go independent) won't affect Haitian internal politics; they might not even affect the American Civil War too much.