Return of allotment is governed by section 75 and this section is applicable to both equity and pref shares allotment. Further form-2 also applicable to both kind of allotment.
Now kindly appreciate allotment can be made collectively by B.O.D. and not by any 1 person even if he is auth by board. Hence a person can not be auth to allot share whether pref or Equity on behalf of B.O.D.
Regarding passing of resolution by circulation I would like to say that there are certain sections in Companies Act which required that resolution should only be passed in BM. For example in section 262 there is a specific wording to the effect that casual vacancy be filled by board of directors at a board meeting. Hence resolution by circulation u/s 289 is not applicable to section 262. There are certain other examples also. Check any law book.
But as far as section 75 is concerned allotment can be done by circulation as there is no restriction placed by Law.
But use of section 289 is not easy. First of all read & understand the section properly and its documentation. I would suggest hold a proper BM and pass the necessary resolution for allotment and
if possible set a paper BM and pass the necessary resolution for allotment and file form-2 within 30 days. Regards Ankur