LiPo charging circuit to supply 1mA peak current, to charge a custom 1mAh LiPo cell
You can try to make your own charging circuit based on LM334 constant current source. Maybe. It's just my first idea. You need to sense battery voltage all the time to avoid overvoltage. And LM334 is, as it stands in its name, provide constant current. When battery reaches 4.2 you have to go to constant voltage mode, where current must fall, which is a tricky part. Don't have a solution for it.
Maybe you can do something with LM317 in current limiter mode. Again, you need battery voltage control. But since LM317 is not a constant current source but a current limiter, it has to be able to do both CC and CV if you can manage to limit it 0.5ma.
And you can always have LM317 having higher current limit if you can't set it that low, but you can load it with constant current source LM334. For example, you can have LM317 set for 1ma max current and connect 0.5ma LM334 to it. So battery current will go up to 0.5ma. This is inefficient of course, so depends on how critical it is.
These are just random ideas straight out of the head, there probably are smarter ways.