Maybe a way to do this would be through a conflict of interest between France and England.
Basically you had England on the North (Egypt) wanting to create a Cape-Cairo axis, and France on the East and West, controlling the main port of Ethiopia (Djibouti) and wanting to create a Djibouti-Dakar link.
The king of Ethiopia manages to play one against the other to attract foreign investment and education. These foreign investments offer large shares to the local nobility, thus soothing them into advancing in the modern age (as I understand them, they were the biggest slower of Ethiopian progress at the end of XIXth century IOTL).
Ethiopia agrees to lend passage to the Cairo-Cape axis and the French lines through a technology transfer agreement. As a stable state with access into the deep Hinterland of the continent through the Suez canal, Ethiopia is at a strategic position. They have enough arable land, timber and other resources.
It might work because the UK really really wants that Cairo to Cape line and a solid Ethiopia solidifies their Egyptian deep south and a stronger, richer Ethiopia means more transit through the French port of Djibouti, which means more tax revenues.
Could work- but you'd probably end up with Ethiopia becoming a Thailand analogue with this option, rather than a true Meiji Japan analogue. The best option, IMHO, would have been a more complete victory for the Ethiopians over the Italians in a different First Italo-Ethiopian War- say, if Ethiopia had entered its equivalent of the Meiji Era a lot earlier. Post 1900's almost certainly too late- the best opportunity for them to have done IOTL would have been back in 1868, with the 1868 Expedition to Abysinnia ITTL serving as Ethiopia's equivalent of Commodore Perry's expedition to open up Japan in 1853 IOTL- in this instance, the POD would be the Abysinnian army holding their solid defensive positions on the plateau at Arogye rather than launching a futile suicide attack against the British expeditionary force, with a stand-off developing between the two armies, followed by the calling of a truce and the eventual resolution of the situation via the signing of an unequal treaty, akin to the
Convention of Kanagawa.
Alternatively, you could have a slightly earlier POD, and avert the cause of the 1868 Expedition to Abysinnia. IOTL, this commenced after the British Consul in Ethiopia, Captain Charles Duncan Cameron, had delivered Emperor Tewodros a royal letter and presents from Queen Victoria in person, arriving at Gondar 23 June 1862, and reaching the Emperor's camp that October. Delighted, Tewedros II wrote a return letter to Queen Victoria as a fellow Christian monarch, asking for British assistance in the region. Tewodros asked Cameron to carry the letter back to Queen Victoria personally, requesting skilled workers to come to teach his subjects how to produce firearms, and other technical skills.
Cameron traveled to the coast with the letter, but when he informed the Foreign Office of the letter and its contents, the Foreign Office instructed him simply to send the letter on to London, instead than take it himself. He was to proceed to the Sudan to make inquiries about the slave trade there. After doing this, Cameron returned to Ethiopia. On Cameron's return, the Emperor became enraged when he found out that Cameron had not taken the letter to London personally, had not brought a response from the Queen, and most of all, had spent time traveling through enemy Egyptian and Turkish territories.
Cameron tried to appease the Emperor, saying that a reply to the letter would arrive shortly. But it didn't; the Foreign Office in London never passed the letter on to Queen Victoria, but simply filed it under
Pending. The letter stayed there for a year, before the Foreign Office then sent the letter on to India, because Abyssinia 'came under the Raj's remit'. And apparently, when the letter arrived in India, officials filed it under
Not Even Pending, where it would be lost forever.
After two years had passed, and Tewodros had not received a reply, he imprisoned Cameron, together with all the British subjects in Ethiopia and various other Europeans, in an attempt to get the queen's attention. His prisoners included a missionary named Mr. Stern, who had previously published a book in Europe describing Tewodros as a barbaric, cruel, unstable usurper. When Tewodros saw this book, he became violently angry, pulled a gun on Stern, and had to be restrained from killing the missionary. Tewodros also received reports from abroad that foreign papers had quoted these European residents of Ethiopia as having said many negative things about him and his reign.
The British sent a mission under an Assyrian-born British subject, Hormuzd Rassam, who finally came with a 'reply' from the Queen- which wasn't actually a reply to Tewedros' now three-year-old letter requesting aid at all, which had long since been lost in the mail, but a wholly new and unrelated message, sent in the hope of resolving the hostage situation peacefully. However, Tewedros understandably assumed that this was Queen Victoria's long-awaited reply to his letter. Deeply insulted by the British failure to bring the skilled workers as he had requested, and presumably also by the oblivious and obnoxious tone of Queen Victoria's message ("There's not even any mention of my reply at all! Does she think she is too big, too high and mighty to even acknowledge the message that I sent her, almost FOUR YEARS AGO now? I am Emperor Tewedros II of the Ethiopian Empire! Son of David and Solomon! Where does she get off, blanking me like this? I DEMAND A RESPONSE!") Tewodros had the members of the Rassam mission added to his other European prisoners, thereby providing the cassus-belli for the 1868 Expedition.
So, for a potential POD, WI Captain Charles Duncan Cameron had actually done as instructed, and returned to the UK in order to present Emperor Tewedros II's reply to Queen Victoria in person? Or at the very least, if the guilty culprit in the British Foreign Office had actually done their job and forwarded Tewedros' letter on to Queen Victoria when they actually received it, instead of simply shunting it off into the filing cabinet under 'Pending'?