The Ethopian Army during the First Italo-Ethiopian war had a large amount and variety of semi-modern and modern firearms. Where were they getting them? Did the colonial powers of Europe allow for the sale of such arms and munitions to an African Nation?

Their guns were made in Europe and the USA. Some came direct from Western powers, and others were captured from Egypt.

The Emperor responsible for the first major modernisation of the Ethiopian armies with modern guns was Yohannes IV. The first major attempts at modernisation were by his predecessor (or predecessor once removed, depending on who is counted as an emperor) Tewodros II (Theodore II), but he made somewhat of a strategic error by getting into a war with the British, and losing it, which led to the loss of both his life and the modern arsenal he had built up. Yohannes had to start essentially from the beginning. His start was prompt, since he was given arms by the British for helping them in their war against Tewodros (about 1000 guns, including 130 rifles, 6 howitzers, and 6 mortars). This beginning contributed to his goal of becoming emperor.

Becoming Emperor, Yohannes imported modern guns as much as availability, money, and the blockade by the Egyptians (who held the coast, formerly held by the Ottomans who also blocked arms shipments to Ethiopia). By the time of his wars with Egypt in 1875-1876, he had approximately 10,000 rifles (and plentiful older guns: percussion muskets, flintlocks, and even matchlocks; older guns like these - including some centuries-old matchlocks - would still be in military use to the end of the 19th century). Fortunately for Yohannes' plans for gun acquisition, the Egyptians were well-armed but outnumbered, and he was able to defeat them and obtained as booty 20,000 Remingtons and 25-30 cannons.

Yohannes' future successor, Menelik, then the ruler of Shoa, was also building up his arsenal of modern guns. Many of these were obsolete - by European standards - rifles, sold by private traders for handsome profits. This trade was encouraged by the French and Italians. The French saw in Menelik a chance to counter British influence (over Yohannes), and the Italians a counter to Yohannes. In 1884, Italy contracted with Menelik to supply 5,000 Remingtons per year for 10 years, and 4,000 Wetterly rifles (immediately). In 1888, with war with Yohannes appearing imminent, the Italian Prime Minister gave Menelik a further 1,000 Remingtons. Needless to say, the British were unhappy with this arming of an enemy of their friend, but the French and Italians refused to desist forthwith, despite British demands.

The expected war with Yohannes did not materialise, since the Mahdists invaded from the Sudan, and Yohannes died in battle. While Yohannes' army had many guns, it was a large army, and spear and sword were still the major weapons, along with muzzle-loading firearms, for both sides. It was the firearms that killed Yohannes: shot. The British were now happier to see arms shipped to Ethiopia, to contain the Mahdists.

Menelik was the best-armed of the potential successors, and became the next Emperor. He continued to import guns as quickly as his finances would allow, and was helped by gifts from European powers seeking influence: about 40,000 rifles and 30 cannons as a gift from the King of Italy, and 10,000 rifles from the Russian government.

Relations with the Italians deteriorated in the early 1890s; this would lead to the fighting at Adowa in 1896, and the defeat of Italy. Arms supplies from Italy stopped, and the Italians tried to stop other European powers supplying weapons, with some success: the German government refused an order for 100,000 rifles. The French, however, continued to supply modern arms, including rapid-firing cannon and machine guns. With the Italians now in the former role of the Egyptians of attempting to block arms supplies, import was more difficult, largely through Djibouti. The Italians estimated that poor transport from Djibouti (largely by camel) restricted Menelik's imports to a mere 25,000 rifles per year.

In summary, the desire for profit, and inter-European rivalry, with powers seeking influence in Ethiopia, allowed Ethiopia to arm well. This was helped by the capture of Egyptian weapons (20,000 very modern rifles + some artillery), but in the end, these captured weapons were greatly outnumbered by imports, both purchased and gifts.

The Osprey book on Adowa (Sean McLachlan, "Armies of the Adowa Campaign 1896: The Italian Disaster in Ethiopia", Men-at-Arms 471, Osprey, 2011) quotes an Ethiopian poem:

What a fool he is, the person from a European country;

How, having made the instrument of death, can he give it away?

With the Vetterli that he bought, with the bullets that he bought,

Menelik roasted and cracked the foreign barley.

suggesting that at least some Ethiopians were surprised by the European willingness to supply arms.

For an excellent review of the supply of guns to Ethiopia, see Pankhurst, R. (1965). "Guns in Ethiopia", Transition, (20), 26-33. doi:10.2307/2934388 https://www.jstor.org/stable/2934388