J C C Mays prints this eight line political squib as Coleridge's (it's #384 in the Poetical Works, 2:794). In his headnote he says 'the only known text of the poem is a transcript by JTC [John Taylor Coleridge] in his Commonplace Book, subscribed "S.T.C." It is likely that the poem was copied from a contemporary newspaper which has not been traced.' Mays adds: 'there is no reason to doubt C.'s authorship, unless JTC merely guessed at it.' There is one reason to doubt C.'s authorship, though: and that's that the poem was actually written by James Sayers. It appears in his All the Talents' Garland: Or, A Few Rockets Let Off at a Celebrated Ministry (1807), a collection of political satires lampooning Grenville's shortlived 'Ministry of All the Talents'.
The poem appears on p.49; that's Sayers' version, at the top of this post. It's odd that Mays doesn't clock this, since he discusses at length whether two further satirical epigrams, 'Two Epigrams on Pitt and Fox' (#389) are by Coleridge, noting that the second of them
Britannia's boast, her glory and her pride,'was published in James Sayers's satirical anthology All the Talents' Garland' and 'appears in JTC's Commonplace Book' [Poetical Works 2:800]. Presumably he happened not to notice that 'The Taste of the Times' is in All the Talents' Garland too.
Pitt in his Country's Service liv'd and died.
At length resolv'd, what Pitt had done, to do;
For once to serve his Country, Fox died too.
The preface to All the Talents' Garland makes it clear that the poems in the volume are all original, and written by 'Polypus' (the preface also makes it plain that this is James Sayers), excepting only those few that 'are taken from that excellent newspaper, the Morning Post' and 'now and then' from 'the able columns of the Evening Courier':
'He', there, is Sayers. As Mays notes, Coleridge 'was connected at this time not with the Morning Post but with The Courier' [Poetical Works, 2:801]; and although the 'Britannia's boast' quatrain had previously appeared in the Post (31 March 1807), the 'Taste of the Times' was not previously published in either the Post or the Courier.
So why did Coleridge's nephew copy the poem into his Commonplace book ascribed to 'S.T.C.'? It's hard to say. It could, simply, be a mistake. John Coleridge first met his uncle in 1811, when he himself had just turned twenty-one, and came to London for a visit (he was to graduate from Corpus Christi, Oxford, the following year). It could be that STC told young John that some of the poems in Sayers's anthology were by him, and conceivably even pointed a few out, which JTC then copied into his Commonplace book; but if so, it's also possible that STC misremembered, or JTC misunderstood.
This in turn raises the intriguing possibility that there are, in amongst the 110-pages of Sayers's volume, other STC-composed verses. One day, when I've the time, I'll go through and check each against prior publication in the Post or Courier, and possibly add hitherto unnoticed original compositions to the Coleridge corpus.