The answer to this question really depends on one's interpretation of the cultural history of the times, and indeed of the cultural hinterlands of people who write on UFOs.

If you're asking whether there were, in the 1800s, reports of things being seen in the sky that shouldn't have been there, or which did things that contemporary aircraft (meaning balloons and early airships) were not capable of doing, then yes, there absolutely were, beginning certainly from c.1880, but most particularly right at the end of the century, in 1897-98 – when there was a well-reported, and still well-remembered, "wave" of mystery airship sightings, a phenomenon that was almost entirely confined to the US, but which popped up again on a worldwide basis from c.1909 with numerous further reports of mystery aircraft and airship sightings in the UK, Europe, Canada, Australia, South Africa and New Zealand. UFO enthusiasts have frequently cited these reports as evidence that the phenomenon they study (and which many of them consider to be physical and to involve visits to earth by alien spacecraft) has a lengthy history. However, studies by historians, folklorists and anthropologists have all preferred to place these early reports in their contemporary cultural contexts.

Seen in this way, the first waves of "UFO sightings" can be re-interpreted as most likely the product of a rich brew of misperceptions of known objects, expectant attention, the influence of popular religion, and the hoaxes that – it has been fairly conclusively shown – contemporary regional newspapers were quite prone to. One key driver of this group of reports was intense interest in progress being made in aeronautical technology; it is especially noticeable that the pre-1900 "airship" sightings involve both reports of encounters with landed craft piloted by human inventors (a "Mr Wilson" is the name most often encountered in this respect) and technology that was one step – but only one step – ahead of what had actually been achieved by this time, rather than, say, the gleaming extraterrestrial spaceships reported after 1947.

The post-1900 waves, in turn, are fairly clearly related to war scares, with reports of both mystery aircraft and mystery airships generally attributed to clandestine flights undertaken by the Germans.

That many, probably most, of these reports had more to do with contemporary expectations, hopes and fears than they did with reports of physical aircraft of some sort is perhaps best shown in the case of the wave of sightings that took place in New Zealand in 1909, and which – to be explicable at all as sightings of actual aircraft – had to be attributed to flights originating from secret German aircraft-carrying ships that we can now be absolutely certain never existed.

Sources

Robert Bartholomew, 'The Quest for Transcendence: An Ethnography of UFOs in America', The Anthropology of Consciousness 2 (1991).

Thomas E. Bullard, The Airship File: A Collection of Texts Concerning Phantom Airships and Other UFOs... (1982)

Jerome Clark, 'Airship sightings in the nineteenth century,' in The UFO Encyclopedia: The Phenomenon From the Beginning, vol.1 (1998)

David Clarke and Andy Roberts, Flying Saucerers: A Social History of UFOlogy (2007)