I am considering my next character to be a changeling with a tiefling parent. A child has a 50/50 chance of being either, when born to a human.
Is there existing lore where a changeling and tiefling have a changeling child?
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While this is not established in 5E, old lore often carries through from older editions if it is not superseded by new lore. So, the only book I'm aware of that talks about Changeling reproduction is the 3.5E book Races of Eberron. From there, we get the following...
Two changeling parents breed a changeling child. A changeling and a humanoid can mate to produce an offspring with the child having a 50% chance to be of either race.
-Page 45 (Emphasis Mine)
Your question noted that there's a 50/50 chance of getting a changeling if they mate with a human...but it's not just human. It's any humanoid. Changelings can reproduce with literally any creature with the Humanoid Type, and there is a 50/50 chance of getting a Changeling, or getting whatever the other parent was. And it is binary...you don't get, say, a Half-Changeling, Half-Bullywug.
It is, perhaps, worth noting that Planetouched (i.e. Tieflings) in 3.5E were not actually considered humanoid. They were 'Native Outsiders.' But they are Humanoids now, and it's not clear in Races of Eberron that this ruling was meant to exclude humanoid-but-not-really races like Planetouched.
YES, most probably
Tieflings have a human bloodline and Changelings have a human bloodline.
So, I have tried to answer your question as far as I can, taking information from D&D 5e sources including Eberron: Rising from the Last War (ERLW), the Player's Handbook (PHB), Xanathar's Guide to Everything (XGE), Mordekainen's Tome of Foes (MTF) and the Monster Manual (MM).
There is no concrete answer to this, but I have made some conjectures based on 5e sources which I hope will be helpful.
First of all, there is nothing to suggest that a Changeling could not have a Tiefling parent. Tieflings "are derived from human bloodlines". (PHB p.42) You can read about 5e lore about Tieflings in the PHB in the section on races and in MTF under the chapter on The Blood War. Also, the subrace described in the PHB has a bloodline to Asmodeous; for other Tiefling sub-races see Tiefling Subraces (MTF, pp. 21-23).
Note: There is no lore in D&D 5e about 50/50 chance of being born a Changeling, so far. This comes form D&D 3.5.
In the lore so far for Eberron in D&D 5e, it is not explicitly said that Changelings themselves must have a human parent, but the human bloodline is strongly suggested in the opening legend described by Chance, the changeling priest, where he talks about the woman, named Jes. In D&D 5e when text refers to men or women it generally refers to Humans. Otherwise, the text would refer to Jes as a female Dwarf for example.
"Long ago there was a woman named Jes, and she had one hundred children. Her rivals conspired against her and swore to kill her children. ]es begged the Sovereigns for help, but their only answer was the wind and rain. In the depths of her despair, a lonely traveler took her hand. "I will protect your children if they follow my path. Let them wander the world. They may be shunned and feared, but they will never be destroyed."]es agreed, and the traveler gave her his cloak. When she draped it over her children, their old faces melted away and they could be whoever they wanted to be. And so it remains. Though the children are shunned by all, the gift of the Traveler protects them still." (ERLW p. 17)
Given that Tieflings have a human bloodline and Changelings most likely, too, I do not see why a Changeling could not be born of a Tiefling parent. Who was the other parent? It could have been a Changeling or a human? Or, even another Tiefling with a Changeling in his/her ancestry? As to the question whether a Changeling might be raised by a Tiefling parent, this is also hinted at in that "Some are orphans, raised by other races". (ERLW p. 17) It does not specify which ones, so Tiefling parent/s would be fine. Obviously the DM has the final say on this.
While working on a backstory I would suggest establishing whether the Tiefling parent is Sedentary or Nomadic.
Growing up with a Tiefling parent who is sedentary might suggest that the family would have mostly likely but not necessarily grown up in a human settlement: "Tieflings subsist in small minorities found mostly in human cities or towns. [...] Sometimes they live among other minority populations in enclaves where they are treated with more respect.*" (PHB pp. 42-43)
A Tiefling is likely to be keenly aware of oppression, segregation and prejudice in the world and might be, for this very reason, all the more protective of their Changling child. For example, they may ask their child to take the form of another Tiefling so that they do not attract more attention. The Tiefling parent is likely to be over-protective as Tieflings generally "are not quick to trust" because "Lacking a homeland, tieflings know that they have to make their own way in the world and that they have to be strong to survive." (PHB p. 43)
If the Tiefling parent is nomadic, the Changeling might find it easier to use their shape-shifting abilities to adapt to the lands in which they travel. The Changeling child could adopt various forms to suit their needs.
"Shapechanger. As an action, you can change your appearance and your voice. You determine the specifics of the changes, including your coloration, hair length, and sex. You can also adjust your height and weight, but not so much that your size changes. You can make yourself appear as a member of another race, though none of your game statistics change. You can't duplicate the appearance of a creature you've never seen, and you must adopt a form that has the same basic arrangement of limbs that you have." (ERLW p.18)
For a Changeling, maintaining their persona could mean the difference between life and death for themselves and/or their Tiefling mum or dad.
Changelings and Doppelgangers
In previous editions Changelings lore points to the inter-breeding between humans and doppelgangers. Interestingly in the D&D 5e Eberron campaign setting this notion is not quite the same:
Spawn of Daelkyr - Most of the aberrations on Eberron are the creations of the daelkyr. The daelkyr are masters of flesh-shaping,and they altered existing life forms -often beyond recognition- to create soldiers for their wars [...]
Doppelgangers - The daelkyr Dyrrn the Corruptor enhanced the latent psychic abilities of changelings to develop doppelgangers, while implanting a desire to cause chaos in the communities around them.-even when there's no benefit in it for the doppelganger. Some doppelgangers, driven by visions from the daelkyr, can be found working with the Cults of the Dragon Below or fighting alongside aberrations in Khyber. Others operate alone. (ERLW, p. 284)
In D&D 5e, outside of the Eberron campaign setting, Changelings are described in the Monsters Manual under Doppelganger. But this is not to be confused with the actual Changeling race appearing in Eberron.
"Changelings. Doppelgangers are too lazy or self-interested to raise their young. They assume attractive male forms and seduce women, leaving them to raise their progeny. A doppelganger child appears to be a normal member of its mother's species until it reaches adolescence, at which point it discovers its true nature and is driven to seek out its kind to join them." (MM p. 82)
In conclusion, given that both Tieflings and Changelings have a human bloodline and the lore so far in 5e, it would suggest that YES, a changeling be indeed be born from a Tiefling parent.
In the end, it is up to your DM to decide what story of origin or lore best suits the campaign.