What was the only African country that took part in the Berlin Conference of 1884-85; Liberia, Ethiopia, Libya or Egypt?

None. This site suggests (and it is corroborated by other sites) that no African nation participated in the Conference.

Between November 1884 and February 1885, diplomats from fourteen countries gathered at the Berlin Conference, organized by Bismarck:Germany, Austria-Hungary, Belgium, Denmark, Spain, the US, France, the UK, Italy, the Netherlands, Portugal, Russia, Norway, Sweden, and theOttoman Empire. The official purpose of the conference was to regulate freedom of trade on the Niger and Congo Rivers. However, the Conference in effect set the rules for the division of Africa among the colonial powers – a future division,for, in 1885, only a quarter of the continent had then been explored andcolonized. Fifteen years later, the entire continent was in the hands of Western powers. Yet no African was invited to the negotiations, or even represented!

https://academic.oup.com/lril/article/3/1/31/2413101/Between-law-and-history-the-Berlin-Conference-of
https://academic.oup.com/lril/article/3/1/31/2413101

What is interesting to note is that Liberia was never under foreign control (although heavily influenced by the US) and Ethiopia(Abyssinia) did not come under Western control having successfully held off the Italians. I believe they were the only two independent nations.

https://en.wikipedia.org/wiki/Berlin_Conference

King Léopold II was able to convince France and Germany that common trade in Africa was in the best interests of all three countries. On the initiative of Portugal, Otto von Bismarck, German Chancellor, called on representatives of Austria–Hungary, Belgium, Denmark, France, the United Kingdom, Italy, the Netherlands, Portugal, Russia, Spain, Sweden-Norway (union until 1905), the Ottoman Empire, and the United States to take part in the Berlin Conference to work out policy. However, the United States did not actually participate in the conference. The Berlin Conference took place in 1885.

https://en.wikipedia.org/wiki/Berlin_Conference

It is also almost true that Liberia and Ethiopia were the only independent African nations at that time. But then there was Sudan, which actually was an independent state 1885-1899.

Independent states
Liberia, founded by the United States' American Colonization Society in 1821. Declared independence in 1847.
Ethiopia (Abyssinia), had its borders re-drawn with Italian Eritrea and French Somaliland (modern Djibouti), briefly occupied by Italy from 1936-1941 during World War II's Abyssinia Crisis
Sudan, independent under Mahdi rule between 1885-1899

https://en.wikipedia.org/wiki/Scramble_for_Africa#Independent_states

The conference had ambassadors and representatives from 14 countries/ empires in attendance. It opened on 15th November 1884 and concluded on 26th February 1885 when the General Act of the Berlin Conference on West Africa was signed:

[the 14 countries represented were:]
Her Majesty the Queen of the United Kingdom of Great Britain and Ireland, Empress of India; His Majesty the German Emperor, King of Prussia; His Majesty the Emperor of Austria, King of Bohemia, etc, and Apostolic King of Hungary; His Majesty the King of the Belgians; His Majesty the King of Denmark; His Majesty the King of Spain; the President of the United States of America; the President of the French Republic; His Majesty the King of Italy; His Majesty the King of the Netherlands, Grand Duke of Luxemburg, etc; His Majesty the King of Portugal and the Algarves, etc; His Majesty the Emperor of all the Russias; His Majesty the King of Sweden and Norway, etc; and His Majesty the Emperor of the Ottomans
[signatories:]
Signed by the representatives of the United Kingdom, France, Germany, Austria, Belgium, Denmark, Spain, the United States of America, Italy, the Netherlands, Portugal, Russia, Sweden-Norway, and Turkey (Ottoman Empire).

http://www.sahistory.org.za/archive/general-act-berlin-conference-west-africa-26-february-1885
africafederation.net/Berlin_1885.htm webpage no longer exists