The English word "demon" has been found throughout the New Testament in modern bible translations since the 19th century. However, in the 16th and 17th century and earlier (Tyndale Bible, Geneva Bible, King James Bible, Douay-Rheims Bible) "demons" are not found. They use "devils" rather than "demons". (the Tyndale Bible and Geneva Bible use "deuils" rather than "demons"). This is where the Greek Versions and Latin Vulgate indicate "daemonia".
As expected, "diabola" from Latin, and Greek, also gets translated as "devil" in the old English versions, which is still done in modern translations.
There is one peculiar exception, the Douay-Rheims Bible does use "demons" just one time: in Isaiah 34.14. That verse seems to be referring to wild desert animals rather than evil spirits, and modern Bible translations don't use the word "demons" in that verse. In the Clementina Vulgata, "daemonia" is used in that verse in Isaiah, but in the "1979 Nova Vulgate" the verse specifically refers to wild desert animals (rather than demons) making it compatible with modern bible translations modern translations. Otherwise, "daemonia" is repeated in a number of verses in the New Testament in both (old) Clementina and (new) Nova Vulgate editions.
The King James Version has zero references to demons. They are always mentioned as "devils" when the Greek and Latin indicate daemonia is used. However, the word "demonstrate" is found in the King James version, so the root word was in use.
I'm thinking that "demons" did not enter the English vocabulary (as an evil spirit) until the 19th century. In 1833, Noah Webster translated the Bible using "demons" rather than "devils" (for evil spirits in the New Testament) for the very first time in a signification Bible translation (that I can find).
I'm thinking that "demon" and "demons" were introduced into the English language as a wild animal, probably wild desert goats, which in the Gospel, were inhabited by "demons" according to Modern Bible translations. (they were inhabited by "devils" according to King James and Douay Rheims, and "deuils" in Tyndale and Geneva Bible translations. I'm trying to find out when demons were first used to refer to evil spirits in popular English, because it doesn't appear that it was in popular use back in the days of King James.