I guess another option is to work to increase the population again. There's no implicit reason why Japanese couldn't have more children (the immigration option does seem to be off the table).
[1] http://magazine.good.is/articles/robots-elder-care-pepper-ex...
If the social safety net becomes weaker (which one would expect if its current strength becomes demographically untenable), then immediate family in the next generation becomes the dominant personal safety net, and larger family sizes are incentivized (its basically one of the processes that led to declining birth rates in the developed world running in reverse, as social safety nets weaken rather than strengthening.)
Note that I'm not saying this is painless, as its a social change which is very slow and lagging the driving force.
It requires a cultural shift. But those kinds of shifts do happen, particularly when they make sense and have the support of the government. After WW II a number of countries promoted large families, and that's what they got.
>It's far more likely the politicians and/or society as a whole will come to its senses and start promoting immigration, but I don't really see that happening either.
Whether that constitutes "coming to its senses" is really a question up for debate. Mass immigration is trading one set of problems for another. They might be substantially worse off.
So the people that you need to make babies, first are naturally less inclined, and even if they are, they live in a very expensive environment. The older generation that could help them don't even live close by so that one additional complexity.
Then there are some Japan specific stuff like the stupidity bad work-life balance. That was bad with single worker family, but that just not feasible when both parents are working.
There is a lot in there that is in the power of the government to help. Free nurseries, quality schools in cheaper area of big cities (note it is useless to give help to buy, just help people where they are instead). Cheap activities to keep the kids occupied during the holidays. Tax breaks. Penalising overtime. Lots of media coverage - having a kid should look something desirable.
There is a trend, Japan won't beat the trend, but right now they are way worse than the rest of the world and they can definitively do something to get back in the pack.
edit: Thinking as a parent. There are a lot of practical difficulties with children that are difficult/expensive to overcome when both parents are working: school and nursery time - generally they open way after you need to be at work and close way before, especially school. Here in the UK, school close a whole 3 hours before either my wife or I stop working. What am I supposed to do short of having relative to care of them, we will need to pay a private school where they offer to keep them a bit longer for a ridiculous fee on top of ridiculous admission cost.
Far from the worst. And the European countries in the link are artificially propped up by immigrant births; their true citizen birth rate is even lower.
http://data.worldbank.org/indicator/SP.DYN.TFRT.IN/countries...
http://www.ft.com/cms/s/0/32788ff0-ea00-11e3-99ed-00144feabd...