I would just invite a coupele of his friends for a play date for his bithday, Just tell the other mums that its not a party just a catch up? That way there is no pressure of that kind of thing?
I think you could say something like the above.
TBH though I would probably still be prepared to pay for the other children's entry. From an "invitee" perspective, if you are invited to a playcentre for a playdate for no special reason, it's easy to say no if you couldn't afford it, or suggest another place, if you are invited for a child's birthday I'd feel like I couldn't really say no therefore I think it could create resentment having to pay.
Are you very close with the parents of the other kids? If the parents are very close friends I think it could totally work as you can talk openly about these things, if they are the friends from preschool or something like that where you don't really know the parents, it might be more awkward. Are these people that you would normally catch up at a playcentre with anyway?
I'm not sure how much playcentre entry is (I'm guessing around $15?) so if money was tight I would rather invite just 2-3 friends, bring my own cake and make it a very casual playcentre party... $45 is not that much to spend.
Other options would be just having the same kind of thing in a park- then you could invite as many of his friends as you want- just call it something like "having a play in the park, and we might bring a cake along".
I have a group of friends who meet regularly in the park for playdates anyway, and when it's been a child's birthday if we want to have a casual birthday we just say "Hey it's X's bday that week, we'll bring a cake"
I think if you only want to have parties certain years then you have to explain that to your child, rather than trying to give him the same sort of party that his brother had, but making other people pay for it IYKWIM