Time and Again
The book is about an artist recruited for a government experiment in time travel, in which the man is sent back to the Manhattan of 1882, where he falls in love while investigating the mysterious circumstances behind a suicide. It's somewhat a cross between 12 Monkeys and Gangs of New York (which was co-written by Lonergan) and involves a mix of romance and historical tragedy that might also lump it in with Titanic. Another more obvious film connection is with Somewhere in Time, which features a character named for Finney (who also wrote the basis for all the Body Snatchers movies).
According to a New York Times article from 1994, the book has gone through many hands, including those of Paul Newman and Joanne Woodward, John Huston, Joel Silver and even Steven Spielberg, and at one time NBC was planning to adapt the novel as a TV miniseries. But budget concerns and the fact that Somewhere in Time bombed have constantly kept the thing from being made.
In all honesty, even with the sci-fi angle and some action scenes involving a building fire and a police chase the film would be light on mass appeal, particularly given that it'd primarily be a period piece love story with a fairly unsatisfying mystery subplot. But anyone who marveled at the re-creations of 19th Century Manhattan in Gangs of New York would similarly enjoy similar set pieces in Time and Again. And the CG effects required to handle such reproductions of NYC in both 1882 and 1970 (for certain reasons, including one that the book doesn't touch on, the 'present' of Finney's novel should be kept) are likely much cheaper, easier and more realistic than they were nearly a decade ago.
My only hesitation in wishing for Time and Again to be made into a movie is that a Hollywood adaptation would probably focus too much on the events of the book and less on the themes, which deal with history, change, the fleetingness of time and memory and the relative pros and cons of different eras (do we prefer to live in a world of vaccines and nuclear bombs or in a world of greater disease yet greater innocence?). But that's something we will always fear in the translations of book to film.
One great thing for Hollywood to consider: if Time and Again is a hit, there's already a sequel written by Finney, who unfortunately died before he could finish a planned third book.