I'm in a slightly odd situation - a) haven't had the baby yet, b) I'm supply... we sat and did the numbers long before I got pregnant and it's not economically viable with how supply's dying year on year (this year's been utterly terrible) for us to pay out for childcare in order for me to continue working - so I'm currently seeing out a few pre-existing bookings and then stopping altogether (can't say I'll miss agency smarm and lies much really).
We can just about afford-ish to live on one income - but what I've been doing for a few years is a mixture of test marking and tutoring. I mark KS2 SATs (well I ain't this year since the baby's due right when they're sat), but that's a less secure contract these days with the changes to English - I got offered a contract to mark reading tests only but have had to turn it down this year - I applied for that back when ETS screwed up the tests that year - but Edexcel have taken back the running of it in recent years and I think you just apply to be an assessment associate on their website from what I recall (need your work history and references basically). I've got relatives who are secondary who GCSE mark and they applied through the relevant examining boards in a similar way.
Prob too late for this year's SATs anyway - the contracts went out earlier this week and you tend to have to do a couple of years as a reserve marker before you end up getting a full allocation - either way you have to do the training day (which is pretty heavy going but you do get a nice lunch normally) and get paid for that, plus the standardisation and benchmarking scripts you also get paid for.
The other thing I do which has gone ridiculously nuts in demand this year is private tutoring. I plan on stopping that just before the baby arrives, taking a break for the summer and restarting a light load in September, with a view to building that up as a proper business instead of just a sideline as the bump gets older (really should get down to deciding a name lol). Getting started's trickier - I get a lot of business via an agency which is mildly annoying since I have to pay commission per lesson I teach on that business - but it snowballs and word of mouth starts to spread as time goes on - I get phonecalls now from people who've got my number from friends whose children I tutored 2-3 years ago. I do 2 evenings a week - one of a couple of hours and one of one hour, one Saturday morning and get a couple of hundred quid a month out of that - I've had so many enquries this year though that I could have filled every evening a week with kids within about a 10 minute drive of me. I've now got parents trying to book their younger siblings in for next year already!
Tends to die off during the summer after exams and SATs get sat - but sometimes you pick up the odd child whose parents just want someone kept on their case during the summer holidays so they don't slack off which keeps things going then. Tends to be I get a flurry of phonecalls first few weeks in September (usually when the first maths homework of the year goes home and parents can't do it), and again after parents evenings - but like I say, this year it's gone insane - I've turned quite a lot of people away (but I tend to pick and choose quite carefully who I take on as there's nowt worse than plodding away for an hour with a kid and family you've got no rapport with).