Well, folks, looks like we're out of luck on finding the Toners on the 1880 census. In 1870, according to the Brooklyn Eagle blurb about Richard's attempted suicide, they're living at 91 Verona St. The 1879-1880 Brooklyn City Directory lists the Toners at 267 Van Brunt St. The 1881 Brooklyn City Directory lists them at 84 Tremont St. It appears they were moving a lot at the time. Remember, Richard had formerly been worth a lot of money. (Related? Who knows.)
They don't show up in the name index search for the 1880 Census, and in looking at the addresses in question, they're not listed at either 267 Van Brunt St. or at 84 Tremont St. My conclusion is that they were moving right around census time, so the census missed them - they enumerated Tremont St. before the Toners had arrived there, but Van Brunt St. after they left. Of course, it's possible that they were missed for some other reason, or that they were living at yet a third address between 1880 and 1881, and for some reason (name spelled wrong?) aren't showing up in searches of the index. Beginning in 1882, Richard Toner no longer shows up in the Brooklyn City Directories I've seen. I'm thinking that that is potentially around when he died, but I can't know for sure.
Our next recourse are the NYS census records - state censuses (as opposed to federal censuses) were taken in 1875 and 1892 (relevant to this search) as well as in 1855, 1865, 1905, 1915, and 1925. I'd like to see them all, but especially the 1875 and 1892. They're not online, but are available on microfilm at the NYC Municipal Archives, as well as, potentially, on microfilm at Family History Centers across the country. If the latter, I've been meaning to try to get to one of those near DC. If only the former, I'll try to get to it this summer, or the next time I'm in NY and have some time to kill on a weekday.
(Also, the Toners seem to stop showing up in the Brooklyn Eagle around the end of the 1870s, which makes me think that it was one individual - probably Richard - who submitted their news items, and when that person died, so did the Brooklyn Eagle submissions. Again, just a theory.)