Unions said Camara's appointment last month violated a power-sharing deal aimed at wresting some political control from the president.
Scores died in clashes with security forces and rioting after Camara was named and unions restarted a nationwide strike calling for Conte to step down.
Day of prayer
The unions called off the strike on Sunday after the president agreed to replace Camara with a more independent prime minister.
Ibrahima Fofana, a union leader, had declared Monday a day of prayer for the more than 100 people killed in political violence this year, mostly in confrontations with firing security forces.
Kouyate has worked mostly for international organisations serving West Africa.
He was most recently based in Ivory Coast, where he represented the International Organisation of Francophone countries.
He has also worked for the 15-member Economic Community of West African States and the political affairs section of the United Nations.
Martial law
Union representatives could not immediately be reached for comment on Conte's choice.
Strikes this year have crippled Guinea's economy, shut down the port and pushed up prices for key commodities.
The unions have complained of economic problems and demanded salary increases and arrears of months of unpaid wages.
After January's strike turned bloody with security forces firing on demonstrators and killing dozens, Conte agreed to appoint a new prime minister with increased powers.
Instead of naming a consensus premier, Conte selected Camara.
Angry youths took to the streets again upon hearing their president's choice and unions resumed strikes on February 12.
Conte responded by imposing martial law the same day. The move included a curfew, roadblocks and military searches across the country for two weeks.
The government ended the emergency law on Friday after politicians, in a rare show of dissent, unanimously rejected the president's request to extend it.