The direct cause of the Triple Alliance War was the Brazilian intervention in the Uruguayan Civil War(1863?-1865). López had pledged to help the Uruguayan government, and when the Brazilians invaded, he invaded Brazil(bad move). Remove the Brazilian intervention(not hard; the whole episode was caused by large ammounts of people involved screwing up), and you avoid the war.
Incidentally, you probably get a Paraguay-Brazil war later on, with probable causus belli the disputed border between both countries. Surprisingly enough, this is a war Paraguay might win; the Mato Grosso province was virtually isolated from the rest of Brazil, its only access the Paraguay river(a railroad connecting Mato Grosso to the rest of the country was only concluded in 1910); without Argentina as a stage-out ground, reaching Paraguay is much harder(it was tried once during the war; an expedition from São Paulo reached Mato Grosso and invaded Paraguay from the north; it failed, with casualties being some 2/3 of the original number, the vast majority to disease).
