The earliest banjos were strung with whatever fiber was available - horse hair, linen, sinew, rawhide... The intestines of small animals, when cut into strips and dried, create a particularly strong and resonant string. These "gut" strings became the standard and persist to this day. Sheep intestines are the most common source for today's banjo strings. In the minstrel period from the 1840s to the advent of wire strings at the end of the 19th century, banjos were strung with gut.
All the classical string instruments of the 19th century used gut strings and so they were readily available. Fiddle strings often appear on inventory lists of even the frontier fur trading posts. Up to and including the post civil war period however, I have only ever found one reference to wire or metal strings on the banjo, the guitar or the violin. The reference comes from an advertisement in the Trinity college Yearbook of 1895 for a steel string "Banjay" which also included a waterproof head.
In the 1890s steel strings begin to come into their own and musicians begin experimenting with them. These "wire strings" ruined so many guitars that some of the early guitar makers issued warnings at the time of sale that they would not stand behind these instruments, if they were strung with wire. The 19th century instruments were stressed for gut and guitars designed to accommodate wire strings do not become common until the twentieth century.
This is not to say wire strings did not exist at an earlier date. They most certainly did in Ireland at least. There were wire string harps in the 16th and 17th century, but they were rare and very expensive. I have been able to find references to piano wire as early as the 1830s and 1840s, but the smallest diameter I have been able to document is 0.734 mm in Vienna circa 1840.* Though suitable for a piano or perhaps a dulcimer, that is a very thick gauge for use on a banjo. For comparison, 0.010 to 0.026 mm is the dia. of modern banjo steel trebles. The modern wound 4th or bass string is approx. 0.026 mm. In 1878 with the introduction of mechanical wire machines in America, lighter gauges became possible and economically available. One should note however, that lighter gauge is a relative term. All steel strings up until the 1950s were heavy or at least medium gauge by modern standards. Modern light gauge and strings do not become common until the 1960s.
I have found references to silver wound silk core bass strings for the guitar and in fact this is still a common practice for stringing antique low tension instruments. Nowadays, because of the price of silver, other metal alloys are often used. But even in these early instances of silver wound silk bass strings, the trebles on the guitar remain gut until the very late 19th century.
In the 1890s leading up to WW1 musicians began to turn to wire for the "E" string of the violin. There were a few reasons for this. One was the novelty of the new louder and brighter sound that wire afforded, but the other reasons were strength and durability. Gut during this time period greatly declined in quality and violinists found their E-string frequently breaking during performances.
The problem with late 19th century (post 1878) gut strings is that there was a change to mechanical polishing from hand polishing. Because many of these early strings had some minor highs and lows along their diameter a mechanical polisher would polish too much in the thicker areas and too little in the low areas. This weakened the string in the over-polished areas.
Skilled string polishers of the pre-mechanical polishing age could accommodate the slight variations, so the earlier gut strings did not have these weak points. In recent times, a return to polishing to the true center of the string, the gut strings today are the equal of the finest hand polished gut of the 18th and 19th centuries.
Modern gut strings are now rectified and finished to tolerances never dreamed of by the early craftsmen and many concert musicians are again returning to gut for their unique sound properties. Aquila Corde has produced polymer strings (Nylgut) which approximates the characteristics of gut and it takes a practiced ear to tell the difference. These Nylgut strings have a softer texture and lower tension than most regular nylon guitar strings and are particularly well suited for replica rawhide banjos. They have the added bonus of being inexpensive, especially when compared to rectified gut strings. A single gut string can cost more than a whole set of Nylagut strings.
* This information on piano wire gauges comes from Swenson's Piano. They provide restoration services for vintage pianos and have done extensive research on this subject.