There’s some easy stuff at the Metropolitan Cantor Institute, though my memory fails if it’s in parts or not. Sorry if it’s not.

Here are some possibilities in English, from the Orthodox Church in America:

https://www.oca.org/liturgics/music-downloads/nativity-of-christ
https://www.oca.org/liturgics/music-downloads/annunciation-of-the-theotokos
https://www.oca.org/liturgics/music-downloads/theophany
https://www.oca.org/liturgics/music-downloads/december
https://www.oca.org/liturgics/music-downloads/january

I can help with anything off of the MCI site. If you are not familiar with it, is like CCWatershed or Musica Sacra but for the Ruthenian Byzantine Catholic Church. The tradition with this repertoire is that the congregation spontaneously sings in parts, they call it "natural harmony" and the first component added to a melody is often simply parallel thirds. Below is a hymnal that has some of their Christmas carols in it.

https://mci.archpitt.org/sheetmusic/general/ByzantineCatholicHymnal.pdf

Here are some that seem like they would be easiest to do with two equal voices, and suggestions for arranging.

p. 29 - Angels From Heaven
1st measure top voice only.
Bottom will be 3rds throughout, but when melody has F, then unison.
The second "Have no fear!" can be the same melody as the first.
Tempo is moderate.

p. 32 - God's Son is Born
Bottom will be 3rds throughout.
Bottom should use E# / E when melody has G# / G.
Tempo is moderate or a little slower to start with, in cut time.
Slightly faster on "Now the angels sing their pray'r" and then slightly faster again on "Sheep and oxen gaze".
The G at the end of the 1st phrase isn't used for the Slavonic.
"Sheep and" can be sung as a dotted rhythm.

p. 33 - Heaven and Earth
1st measure top voice only.
Tempo is moderately fast.
Bottom will be 3rds throughout, but when melody has F, then unison.
In the refrain, unison for the phrase "Wise men gifts are bringing".
"Wise men" can be sung as a dotted rhythm.

p. 37 - Joyful Tidings Come Our Way
Bottom will be 3rds throughout, note that below an E in the melody will be sung a C#.
Bottom should use G# / G when melody has B / Bb.
Tempo is fast, and slightly detached articulation works for the first line.
At the end of the repeat of the 2nd line, a dramatic fermata and breath is a good idea, before continuing in tempo.

If you want to sing the Slavonic as well (try it!), there is a pronunciation guide in the front of the book. Vowels sung as in Latin works fine, including Y as "ee" (or modify to something like English short i or short e, depending). Also, note in the Cyrillic alphabet there is a letter for the sound shch, as in "parish church", that is a fun sound.

Very helpful, thanks to you all!