Balfour became Prime Minister on 4 February 1913, following the resignation of Asquith. The members of his cabinet were as follows:
Prime Minister: Arthur Balfour
Lord Chancellor: Lord Finlay
Lord President of the Council: Lord Lansdowne
Lord Privy Seal: 4th Marquess of Salisbury
Chancellor of the Exchequer: Andrew Bonar Law
Foreign Secretary: Austen Chamberlain
Home Secretary: Walter Long
First Lord of the Admiralty: Lord Newton
President of the Board of Agriculture and Fisheries: Earl of Selborne
Colonial Secretary: Earl Curzon
President of the Board of Education: James Hope
India Secretary : Lord Robert Cecil (he was an MP)
Chief Secretary for Ireland: Sir Edward Carson
Chancellor of the Duchy of Lancaster: Earl of Derby
President of the Local Government Board: William Hayes Fisher
Postmaster-General: Arthur Steel-Maitland
Scotland Secretary: Earl of Kintore
President of the Board of Trade: Ernest Pretyman
War Secretary: Arthur Lee.
Selected junior ministers:
Attorney-General: Sir Frederick Smith
Solicitor- General: Sir George Cave
Paymaster-General: Henry Foster
Financial Secretary to the Treasury: Willam Bridgeman
Parliamentary Secretary to the Treasury (Government Chief Whip): Lord Edmund Talbot (he was an MP)
Under-Secretary Foreign Office: 5th Marquess of Bath
Vice President Department of Agriculture and Technical Co-operation for Ireland: Thomas Spring Rice, 2nd Baron Monteagle (1)
Parliamentary Secretary Board of Trade: Stanley Baldwin.
Balfour's government was a mixture of men who were in his previous administration of July 1902 to December 1905, and new men. The most unexpected apppintment was Carson as Chief Secretary for Ireland. He was not entirely trusted by the Ulster Unionists. He was not one of them, being Conservative MP for Dublin University and not a member of the Orange Order. Also the
Belfast News-Letter revealed that his cousin, Maire Butler, coined the name Sinn Fein for that political party. In this timeline there was not a third Home Rule Bill, so no Ulster's Solemn League and Covenant, with Carson as the first signatory.
(1) Here is his entry in Wikipedia:
http://en.wikipedia.org/wiki/Thomas_Spring_Rice,_2nd_Baron_Monteagle_of_Brandon.