There are plenty of modern factory rifles around in cartridges suitable for African use, most chamber for 458 Win Mag. From your inquiry it appears you want to make up a rifle for a classic nitro express cartridge, which the 458 Win Mag is not, so not sure why this cartridge has come into the conversation. None of the American produced African cartridges fit the description "Nitro Express" as it originally came to being.

The early British big bore cartridges using smokeless nitrocellulose powder as opposed to black powder were called Nitro Expresses and many of the 40-50 calibre big bores rimless cartridges can be made on the standard length M98 action. The 404 Jeffery is probably the most 'famous' of these cartridges than can be relatively easy fitted although as pointed out by others, so can the 416 Rigby although it really stretches the standard actions.

I don't know that I have heard the 375H&H called a nitro express although it came out in the same era as the 404 and 416 so earns the right if it hasn't already got it.

PS it is a Nitro Express.