AXI-S is better if you know that you will have a continuous steam of data which has a valid end (tlast signal).
If not satisfied with AXI-S, then build your own. All you need to do is to implement the concept of handshaking.
On the rising edge of the system clock, your device(Tx) will inform the other device(Rx) that it has data to send. So you just make a signal HIGH. The other device(Rx) will sample this signal and if HIGH, should send out another reply-signal driving it HIGH to indicate that it can accept the data. If the other device(Rx) cannot accept the data then let this reply-signal remain LOW. Now if the data sending device(Tx) samples this reply-signal as HIGH, just make your data available on the data bus on the next clock cycle.
You are the architect, so you need to compare all available protocol and decide what suites best for your design!