Sounds to me as though a 3-bit counter would do the job.
1) Clock the counter every 15 seconds
2) detect a count of 5 and do an immediate reset (or detect 4 and reset on next clock)
3) feed the red LED from bit 2 of the counter, so red LED is only on for a count of 4
4) feed the green LED via an inverter from bit 2 of the counter
If this does not do what you want, then maybe you should post a timing diagram. Your description is unclear.
Warning - I have not actually tried this circuit, only imagined it in my head - I could be wrong.