Oversubscribed kids' club

[MorningMoaner]

I coach at a kids' sports club. Bookings for each week are online via an app and numbers are limited. For the last few weeks my age group has been full with a waiting list. There's currently no way to expand numbers in this age group. We are working on getting another coach trained but it's going to take time.
Booking is currently first come first served but I am wondering if we should give preference to those on the waiting list the previous week to make sure everyone gets a go?
Situation is further complicated by the fact that quite a few of the little ones have older siblings who also attend. Numbers are lower further up the club and we've noticed that on weeks when their youngest doesn't get a spot the whole family doesn't attend so maybe we should prioritise them?
It's an individual activity so keeping a consistent group to build a team isn't relevant and we have more of a fitness/fun type ethos rather than being highly competitive.
I'd be interested in opinions. First come first served is of course simplest and avoids any accusations of bias, but is it best?

Can you not change it to paying it for the term?

Is there a reason of can’t offer Block booking monthly or per half term?

We're not keen on termly or monthly bookings for a number of reasons which would take ages to explain, but one of which is that we are primarily a Summer activity and also very weather dependent. Demand - and our ability to run sessions - fluctuates significantly week to week, especially in the school holidays. Parents don't want to pay for weeks they can't come and as a small club with only a few volunteers we don't want the time and cost that goes into issuing refunds and so on.