The most recommended ports for Cyprus are Limassol and Larnaca. The general shipping method is RORO (roll-on, roll-off) although the more expensive shipping method of containers can be arranged on request.
Cars and vehicles into Cyprus do not require anything apart from the standard documentation required for exporting out of Japan (export certificate). Provide Cars arranges this.
See here for tax regulations regarding importing a car from Japan into Cyprus. A used vehicle must be no more than 5 years old on arrival into Cyprus. Generally, the higher the engine capacity the higher the tax.