It's called time-division-multiplexing, or TDM. Each transmitter has a specific time to transmit it's payload. So, you need to determine a timing protocol and a means to ensure each transmitter knows the current time, so it can transmit.
The decades old method is called the Aloha method. This was developed so the government agencies on the various Hawaii islands could communicate with Honolulu. In this case each transmitter transmitted whenever it was ready, but then waited for an acknowledgement from Honolulu. If it did not get one, it waited for a random time period and then retransmitted. This continued until the payload was sent and acknowledged.
If I was designing such a system as you want, I would make the one receiver actually poll each transmitter with a message coded specifically for that transmitter and ask for a transmissoin of either data or a message with no data. This can run quite fast.
It includes an example for a master and 2 slaves that can easily be extended to a larger number of slaves.
Wireless problems can be very difficult to debug so get the wireless part working on its own before you start adding any other features.
The examples are as simple as I could make them and they have worked for other Forum members. If you get stuck it will be easier to help with code that I am familiar with. Start by getting the first example to work