No descendants are recorded for Faramir and Goldilocks, but it is known that the line of Thains continued after their time, and so it is extremely likely that they had children of their own.1
When Faramir Took came of age at thirty-three, he married Goldilocks, a daughter of MayorSamwise Gamgee. This was in the year IV 42 (S.R.1463), after which more than twenty years years passed uneventfully until IV 63 (S.R.1484). In that year, Faramir's father ThainPeregrin - who was now ninety-four years old - elected to join his friend Meriadoc Brandybuck and make the long journey southward into the lands they had visited in their youth.
On his departure, Peregrin gave up his claim to the Thainship, and so his heir Faramir became Thain Faramir Took I of the Shire. Of Faramir's descendants, we have no account, but the fact that he is styled 'Faramir Tookthe first'2 implies that he continued the line of the Thains. There must therefore have been at least a Faramir Took II (and perhaps others of the same name) among the Thains of the Fourth Age, but Faramir is the last of the line to be recorded in the histories.
Notes
1
That is, no descendants are directly recorded, but there is a mention in the Note on the Shire Records in The Lord of the Rings of 'the great-grandson of Peregrin'. Though not absolutely conclusive, the strong implication here would seem to be that this same unnamed Hobbit was also the grandson of Faramir and Goldilocks.
2
It might be noted that Faramir's father Peregrin is also styled 'the first', so somewhere among Faramir's successors there must have been at least a 'Peregrin II' and possibly others sharing that name.