There was a period in time right between core memory and solid state where something was developed (I believe by IBM) which was core memory, but layered "thin film" on either a glass or maybe polyester film substrate.
It essentially gave all the advantages of core memory, but could be printed by machine to eliminate the need for hand assembly that standard core memory required. Fabrication was done using something akin to how PCBs are made, coupled with something akin to offset printing (or something like that).
Information about this memory is very sparse; I've encountered a few references about it here and there on the internet, but mainly I've read about it in old computer books contemporary with the time period (mid-to-late 1960s to early 1970s). I also believe you can find an article or two in old issues of Popular Science magazine for the same period (google books has them all online).
Ultimately, though, solid-state won out for many good reasons; it was a case of a technology which - had it came about 5 years or more before, would have taken over the market, but its window was too small for acceptance (and probably there were bugs to work out).
As an aside: If you like this kind of thing, it is very interesting to read about the history of these kinds of shifts in technology. To read about this history of the transition to tube technology (think about how you would represent and generate a carrier wave for radio communication before tubes existed - it was done), then to transistors, then to integrated circuits, then to surface mount from thru-hole.
Then also the transition from hand-wired "rat nest" construction to printed circuits.
But the real interesting parts on all of these transitions happens between the transitions (and the overlaps) - where there exist both side-by-side, plus interesting technologies developed in the transition, anticipating things, dead ends, and in some cases ideas which won't become common until much later when other technology could "catch up" (mainly for assembly or whatnot).
Early integrated circuits, for instance, were actually tiny soldered devices in a "can" or on a ceramic substrate - of very few parts. But they were anticipated by the small modules done prior by companies like IBM for assembly and maintenance of computers (and even before that, with multi-component tube assemblies of an "entire radio in a tube" type devices). There were also such things as surface mount technology being used when nothing else would do: For instance in the Apollo Guidance Computers, early surface-mount technology was used to make it more robust to vibration, and also lighter weight. Also some early integrated circuit tech was used in them as well. All of these things wouldn't become common at the business or consumer level until years later - but the tech was needed ahead of time of course for the purpose; also an example of the space program of NASA pushing the tech envelope that trickled down to consumers.
Check it out if you haven't already and have an interest; I've found it pretty fascinating, as you can probably tell...