Jewish Uganda
There is, believe it or not, an indigenous Jewish community in Uganda. They are called the Abuyudaya. They originated when one of the local warlords, who had some quibble with the Brits, converted to Judaism to spite them. There were once several thousand but the number subsequently dropped to a couple hundred.
Interestingly, he converted in 1919, by which point the Jewish Uganda idea had been discarded by both the Jews and the Brits as impractical. It is safe to say, though, that there might have been some local sympathy for the Jews, if they were to settle there. The Falasha from Ethiopia and the Lemba from Zimbabwe (both Subsaharan African Jewish groups) might also congregate there.
Herzl himself proposed Uganda as a temporary alternative to Palestine, in 1903. Israel Zangwill and Nahum Syrkin threw their weight behind it as well, and continued to support it even after the 7th International Zionist Congress put the kybosh on the idea, in 1905. Support grew for the idea in the following years, due to the pogroms, but the Balfour Declaration put the last nail in the coffin of Jewish Uganda.
Let us assume that the Balfour Declaration never occurred, or that the 7th Zionist Congress accepted Herzl's idea (unlike, I know, but this is a conterfactual history...). Zangwill had the support of Jacob Schiff, a Jewish American banker who, among other things, established the museum that currently puts food on my table. In OTL, Schiff had generously supported Zangwill's other schemes, and I suspect that he would provide the finances for the Uganda Proposal.
The earliest date for which we have census data for Uganda is 1903, coincidentally the year of the Jewish Uganda proposal, so we can say that the black population started out at 1,649,900.
Naturally, the Eastern European Jews who settled in Uganda would speak Yiddish, fulfilling your requirement that the white settlers speak a Germanic language. To survive in such an alien environment, they would need local allies - such as the Abuyahuda, the Falashas, and the Lemba - but would soon overtake them in population (in OTL, Schiff's enterprises brought 10,000 Jews to Galveston. Let's assume that he settled them in Uganda instead).
Between 1882 and 1914, over 75,000 Jews immigrated to Palestine, fleeing persecution in their homelands, but half of them left, finding Palestine no more hospitable. If these dissillusioned Jews went to Uganda, then we would have perhaps 32,500.
So, we start with 42,500 Jews. Not much by any standards, but a start. This population will probably double by 1937, at a healthy growth rate. This is, interestingly enough, roughly the number of Jews who were in Palestine at the time.