Do messages have a visible receiver address of any kind? In that case, you're out of luck. The only way to do make this statistically sound would involve an insane amount of messages, rendering it impossible.

No, of course there isn't a visible receiver address.

You have a list of peers, P1,...,PN, every second, at a specific pre-decided time, slightly fuzzed to avoid timing stuff, you send a message to each of them. If you don't put one in, it's a dummy message chosen at random and encrypted. But if you have a message, you send that at the appointed time.

Consequently, from the outside of the system, from the PoV of someone who does not have the keys, its behaviour is indistinguishable from a system where no one is sending any messagess at all.