I found something from 1949; it's a 4 page article that describes programming for the EDSAC. It's like a book, but whether it counts as one for this question I leave open. In any case, I think it's worth mentioning in any case.
There's one copy I found online, but it's behind a paywall. Fortunately, I get access through my university, so I was able to copy a little from it. (Tell me if you think I missed an OCR error.)
Programme Design for a High-speed Automatic Calculating Machine
By M. V. Wilkes, M.A., Ph.D., The Mathematical Laboratory, University of Cambridge [MS. received 18 February 1949]
A good deal has been written about the design and construction of high-speed automatic calculating machines, but little has been said about the detailed steps which are necessary to prepare a problem for a machine and to obtain a solution– a process which is usually referred to as 'programming'. Such aspects are, however, of primary interest to mathematical physicists and engineers who may be wondering what help they can expect from high-speed calculating machines in their own problems. It is intended in this article to supply some of this information; most of it will be well known to those engaged on calculating-machine development.
As far as details go: reference will be made to a machine known as the EDSAC (Electronic Delay Storage Automatic Calculator) which is at present being built in the University Mathematical Laboratory at Cambridge, although certain complications which are unimportant for the present purpose will be ignored. The same principles will be applicable to other machines of similar type.
Also note that it makes specific mention of things being digital:
The mathematical application of a digital machine can be discussed quite apart from any consideration of its construction.
