Promoter's resignation

Yes he may resign by approval of other existing members

S.168.

According to section 2(69) of the Companies Act, 2013 the term ‘Promoter’ can be defined as the following:

1. A person who has been named as such in a prospectus or is identified by the company in the annual return in section 92; or
2. A person who has control over the affairs of the company, directly or indirectly whether as a shareholder, director or otherwise; or
3. A person who is in agreement with whose advice, directions or instructions the Board of Directors of the company is accustomed to act.

In the Companies Act 2013 there is no any relating to resignation of Promoter.Your case falls in serial No. 2 above but as C has not paid any thing to the Company it can not be said that he is holding 10% shares.

In my view,in your case  A and B should take only a simple letter from C that he willingly does not want to continue in the Company. ( Even there is no provision in the Companies Act 2013 for  such letter but here this is required to avoid future legal complication from C side) and find suitable person who wants to be in the Company and allot 10% shares of C to him after receipt of the Consideration in any mode what ever is decided among them.