What is the designation for an Arrow?

[Buzo]

Here are the identifiers from the FAA.
http://www.ama500.jccbi.gov/at/rduafss/reference/acft_type/piper.htm

just replace piper with any mfg, and you will get there entire listing.

 

[tarp]

DC9 - good list and I hate to be picky but:

Piper designators:
PA-28-140/ Cruiser/ Flightliner
PA-28-150/160 Cherokee
PA-28-151/161 Warrior/ Cadet(*)
PA-28-180 Cherokee 180 (later models known as Archer)
PA-28-181 Archer II (semi-tapered wings)
PA-28R-180/200 Arrow/Arrow II
PA-28R-201 Arrow III
PA-28RT-201 Arrow IV T-Tail
PA-28R-201T Turbo Arrow III
PA-28RT-201T Turbo Arrow IV T-Tail
PA-28-201T Turbo Dakota
PA-28-235 Cherokee 235/ Charger
PA-28-236 Dakota

* Cadet was a special Warrior designed for flight schools and the most rear windows normally seen on the Cherokee series were not cut out of the fuselage.

In General, if the HP value on a PA28 is increased by "1", then the aircraft was designed with semi-tapered or "laminar-flow" wings vs. the "hershey bar" wings of old. Therefore, an Archer with Hershey Bars is a PA28-180 but with semi-tapered is a PA28-181. There is no increase in HP, only a different wing design.

In your list, you were making artificial differences between Arrow IV's and T-tails - ALL Arrow IV's have T-tails and hence have the extra "T" added to the basic model value, just as a T-tail Lance is differentiated from a Saratoga.