In D&D lore, there are indeed tieflings of races other than human. The stats in the Player's Handbook represent human-tieflings, but this does not preclude the possibility that there are others. Ultimately, the tiefling's human-centered nature is a leftover from AD&D 2nd edition, which was considerably more human-centric than later versions of D&D.
In the Forgotten Realms setting, elf-tieflings are known as fey-ri. They are the result of a house of gold elves breeding with demons to create powerful heirs. The tanarukk are orc-tieflings, a race bred for war. Both appeared in Monsters of Faerûn (2001). The wispling is a halfling-tiefling of demonic descent. The maeluth are infernal dwarf-tieflings. Both of these appeared in Fiend Folio (2003).
To stat these up in D&D 5th edition rules (I am unaware of any official 5th edition product which has done so yet), there are three easy approaches:
- Make it a new subrace of tiefling. The Unearthed Arcana article That Old Black Magic introduces the possibility of tiefling subraces, where their Charisma bonus and darkvision are base properties, while its Intelligence bonus, Hellish Resistance, Infernal Legacy, and Infernal langauge are specific to the Tiefling (Infernal) subrace. You could, instead, create an elf-tiefling by starting with the base tiefling's Charisma +2 and darkvision, and adding the high elf subrace's Intelligence +1, elf weapon training, cantrip and extra language.
- Make a new Infernal subrace of your existing race. For example, take the elf base race, and for its subrace abilities give it Intelligence +1, Hellish Resistance, Infernal Legacy, and the Infernal language.
- Simply use the statistics for base tiefling, and simply describe their origin and appearance as the other race. This is the easiest method.
In order to customize these further, the Unearthed Arcana articles That Old Black Magic and Fiendish Options include variant types of tieflings.