The sign gifts, tongues, prophecy, the gift of healing, etc. were operating all through the Book of Acts, and these gifts are mentioned in the letters that Paul wrote during the Acts period. But when we turn to the letters written after the Book of Acts—the 4 Prison Epistles, and the 3 Pastoral Epistles, we find that the sign gifts either aren’t mentioned at all or we see—as with the gift of healing—that they were no longer operating in Paul’s life. What he could do in Acts 28, he could no longer do in Philippians, or in 1 and 2 Timothy. He could heal all the sick on the island in Acts 28:9, but he couldn’t heal any of his closest co-workers—Timothy, Epaphroditus, Trophimus—after the close of the Book of Acts.
The letters were written to groups and individuals to teach on various subjects the recipient needed teaching on. If this were not so, each letter would be very long and very repetitive. 1 Corinthians was written during the period covered by Acts, but then so was Galatians (no mention of tongues), Colossians (no mention of tongues), James (no mention of tongues) and 1 Peter (no mention of tongues) for example. Most important is the fact that 2 Corinthians does not mention tongues, so by your reasoning tongues had ceased completely in the period between 1 and 2 Corinthians, despite Paul teaching on how to use tongues correctly.
Further, Acts was written AFTER the Pastoral letters (unless you hold to the position that the Pastorals are pseudonymous and early 2nd century) and Luke does not downplay tongues, but actually makes it an important part of the story, but makes no mention of the gift ceasing or going to cease, despite being in a position to know that by then.
You are reading a cessation of the gifts where there is no such indication. The Letter to Philemon makes no mention of the Death and Resurrection of Jesus, are we then to suppose that it had ceased to be relevant in the church at that time?
For something to be Biblical it needs to be taught in the Bible. There is not explicit teaching on the gifts ceasing and there is explicit teaching that the gifts were expected to continue (Acts; 1 Co 12 & 14).
There is an old saying: Absence of evidence is not evidence of absence.
I think you need to do a lot better than saying that there is no reference to tongues in the later New Testament, particularly when historically there is reference to the gift continuing well into the 3rd century.
Generally Cessationists believe that the miraculous gifting of the Spirit (not miracles in general done by God) had ended with the close of the creation of the book of Revelation in 96AD. The sign gifts would have been in operation to warn the Jew of the coming judgment upon their temple in 70AD.
The sign gifts WERE in operation to warn the Jew of the coming judgement on their temple as recorded in the gospels... but that is not actually the purpose of the gift of tongues and so is irrelevant to the argument that they ceased.
Whatever Cessationists believe needs to be backed up scripturally (which it is not) and historically (which it is not).
The use of gifts seem to have waxed and waned throughout the ages. For cessationists to be right, there should be no such use of the gifts after AD96, but tongues is mentioned in the Mark 16 longer ending which is generally dated to the early 2nd century, suggesting that tongues were still common and expected then.
Bringing this up to date, with historically verifiable cases (as opposed to vague references that may or may not indicate the usage of tongues). There is Edward Irving's church in the 1800's and the Azuza Street revival of 1906 which was followed by the Pentecostal revival where the gift of tongues (as well as other gifts) spread rapidly throughout the world. Following that there is the Charismatic Renewal of the 1950's and 60's and then the Catholic Charismatic Renewal of the 1970's. From Pentecostalism onwards the gifts of the spirit, including tongues, have continued in operation in a large number of churches, whether they are using them correctly or not (and a lot are probably not).
Cessationists need to explain how and why such groups operated in the Spiritual gifts and have continued to grow churches (in defiance of the general trend of decline) and how that fits with their theory that the gifts ceased after the first century.