The aim of a pump up jockey wheel tyre rather than a solid, is to allow the tyre to ride over stones and other bumps without coming to a grinding halt!, to that end the tyre needs to be soft and nowhere near it's maximum, otherwise you may as well stick with a solid.
I experimented and found something below 10psi I think? but suck it and see, whatever seems to suit is ok, after all, it's not doing 60mph!