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The phrase to kick somebody downstairs is used figuratively to mean: to turn out somebody, to eject somebody unceremoniously or ignominiously.

Hence, jocularly, the phrase to kick somebody upstairs is used figuratively to mean: to promote somebody to an ostensibly higher position where they will be out of the way and less influential in one’s own sphere of activity.

The phrase to kick somebody upstairs occurs, for example, in the following from the column Personally speaking. A wry look at life with Peter de Rosa, published in the Weekend Herald (Dublin, County Dublin, Ireland) of Saturday 1^st March 2003 [page 20, column 4]:

Explaining the Peter Principle

The Peter Principle, formulated by Dr Laurence J. Peter, states that in any hierarchy, all persons tend to rise to the level of their incompetence.
Given time, every post in any institution is filled by someone incapable of doing the job. […]
[…]
Sometimes a promoted manager is so bad he has to be ‘kicked upstairs’. He’ll be no less incompetent but it’s hoped he’ll do less damage. Why not get rid of him? Impossible. That would show up the bosses who promoted him as being more incompetent than he is.

These are, in chronological order, the earliest occurrences that I have found of the phrases to kick somebody downstairs and to kick somebody upstairs:

1-: From the diary of the English antiquary Anthony Wood (1632-1695), as published in The Life and Times of Anthony Wood, antiquary, of Oxford 1632–1695, described by Himself (Oxford: Printed for the Oxford Historical Society at the Clarendon Press, 1894), edited by the Church of England minister and editor of literary and historical texts Andrew Clark (1856-1922) [Vol. 3, page 133]—the following took place in 1685:

Feb. 27, Friday, in the evening the University verses were published in the Universitie with the Address before them. Half the verses that were made for the said book were cast aside by the overseers, Dr <Henry> Aldrich and <William> Jane (appointed by the bishop, with consent from the vicechancellor) so that many scholars who had good verses and took it in scorne were resolved to have them printed by themselves and entitle them Musae repudiatae, ‘Muses kickt downe staires’.

2-: From the memoirs of the Scottish historian Gilbert Burnet (1643-1715), as published in A Supplement to Burnet’s History of My Own Time. Derived from his original memoirs, his autobiography, his letters to Admiral Herbert, and his private meditations, all hitherto unpublished (Oxford: Clarendon Press, 1902), edited by the British historian Helen Charlotte Foxcroft (1865-1950) [The employments given by the king: page 145]—the following took place in 1685, when James Stuart succeeded Charles II as James II and VII:

When Rochester was turned out of the treasury and made lord president of the council (which was a higher place as to precedence, but much lower as to interest) he had said he had known many kicked down stairs, but he never knew any kicked up stairs before.

3-: From a letter, dated 28^th November 1750, that the Countess of Shaftesbury wrote to the British grammarian and politician James Harris (1709-1780)—as published in A Series of Letters of the First Earl of Malmesbury, his Family and Friends, from 1745 to 1820 (London: Richard Bentley, 1870), edited by James Harris (1807-1889), 3^rd Earl of Malmesbury [Vol. 1, page 78]—the adjective Bedfordian refers to the British politician John Russell (1710-1771), 4^th Duke of Bedford:

I find most people are inclined to believe the Ministry are in discord and jealous, and that the Bedfordian set will be honourably kicked up or down stairs. A friend of yours says, he is not a sufficient connoisseur in politesse and ceremonials to know whether a nominal advancement in dignity and post, without power, be up or down; but I know it is generally thought the last, and I believe it will end so.

4-: From a transcript of the debates that took place in the House of Commons on 16^th January 1784, as published in The Parliamentary Register; Or, History of the Proceedings and Debates of the House of Commons (London: Printed for J. Debrett, 1784) [page 598]—the reference is to the British politician Frederick North (1732-1792):

Lord North said, […] the honourable gentleman […] wished him […] to be kicked up stairs. For his part, he had no inclination to be kicked up stairs; […] he would not go to the House of Peers; he would stay in that House, to defend his character and his honour.