Light aircraft instructor pilot reported an NMAC in the pattern at CKZ non-towered airport.

Narrative

We decide to go to CKZ for work at uncontrolled fields. At first we were the only aircraft there. Our first lap in the pattern we had no issues. When starting our takeoff CKZ became very busy. After taking off an airplane announced extended downwind (on the upwind side) for Runway 26. Upon spotting the aircraft it was decided that the best action would be to extend our upwind and follow the spotted traffic after it passes. After the downwind aircraft closed to gap between us on the upwind; we announced we would turn left crosswind for 26 and follow them. After announcing I proceeded to do a full 180 degrees scan from left to right; upon completing the scan on the right I saw another aircraft very close on the right wing and slightly behind us trying to enter the pattern on a crosswind. I immediately banked left to increase the gap between our aircraft. Once the plane passed behind we decide it was best to leave the area to avoid any other possible conflicts. The aircraft entering the pattern should have either used a recommended pattern entry or allowed more space upon hearing the amount of traffic at CKZ. I feel better education on how to enter and announce in the traffic pattern may have avoided the situation all together.