This chart shows when each gift was specifically mentioned in history. The gift of healing, for example, is mentioned as still occurring by writers in AD 177 and 240.

Justin Martyr (165) writes:

• Dialogue 82 - The prophetical gifts are only manifested among Christians and still continue.
• Dialogue 85 - Jewish exorcists make use of craft when they exorcise, even as the Gentiles do, employing fumigations and incantations.
• Dialogue 51,52 - Jewish prophets ceased after John the Baptist.

Irenaeus (177) writes:

• Against Heresies 2.31 - Christians still heal the blind, deaf, and chase away all sorts of demons. Occasionally the dead are raised. Gnostics and other non-Christians can't chase away demons - except those demons that are sent into others by themselves, if they can even do so much as this.
• Against Heresies 2.32 - Some Christians do certainly and truly drive out devils, so that those who have thus been cleansed from evil spirits frequently both believe in Christ, and join themselves to the church. Others have foreknowledge of things to come: they see visions, and utter prophetic expressions. Others still, heal the sick by laying their hands upon them, and they are made whole. Yea, moreover, as I have said, the dead even have been raised up, and remained among us for many years. The church does not perform anything by means of angelic invocations, or incantations, or by any other wicked curious art; but directing her prayers to the Lord.
• Against Heresies 4.9 - In 1 Corinthians 13, "that which is perfect" and "face to face" refer to the second coming. 
• Against Heresies 5.6 - Those who are "perfect" are those who have received the Spirit of God, and who through the Spirit of God do speak in all languages, as He Himself, used  also to speak. In like manner we do also hear many brethren in the church, who possess prophetic gifts, and who through the Spirit speak all kinds of languages, and bring to light for the general benefit the hidden things of men, and declare the mysteries of God, whom also the apostle terms "spiritual," they being spiritual because they partake of the Spirit, and seek spiritual understanding to become purely spiritual. 

Tertullian (200) writes:

• Apology 23 - Moreover, if sorcerers call forth ghosts, and even make what seem the souls of the dead to appear; if they put boys to death, in order to get a response from the oracle; if, with their juggling illusions, they make a pretence of doing various miracles; if they put dreams into people's minds by the power of the angels and demons whose aid they have invited, by whose influence, too, goats and tables are made to divine, how much more likely is this power of evil... The wicked spirit, bidden to speak by a follower of Christ, will as readily make the truthful confession that he is a demon.
• Apology 27 - The whole power of demons and kindred spirits is subject to us.
• Apology 35 - The arts of astrologers, soothsayers, augurs, and magicians were made known by the angels who sinned, and are forbidden by God.
• Marcion 4.22 - The Montanist* book The New Prophecy teaches when God speaks through man a "grace ecstasy or rapture" is imparted whereby "he necessarily loses his sensation because he is overshadowed with the power of God"
• Marcion 5.8 - Tertullian agrees with Montanus* that gifts of the Spirit accompany "ecstasy or rapture" as it is called.
• Soul's Testimony 1.3 - Only Christians can expel demons from people.
  Treatise of the Soul 1.45 Thus in the very beginning sleep was inaugurated by ecstasy: "And God sent an ecstasy upon Adam, and he slept."
• *In his last days Tertullian became a follower of the heretic Montanus, who wrote the book The New Prophecy. Montanus taught he was a second comforter sent by God, spoke in a new kind of tongues and gave false prophecies, all of which the Christians said were demonic.

Origen (240) writes:

• Against Celsus - 1:67 Christians still expel demons and heal the sick.
• Against Celsus  - 2:8 Christian still do miracles and prophesy.
• Against Celsus 7:3 - A true prophet under the control of the Holy Spirit does not fall in to ecstasy or madness like the pagans do. 
• Against Celsus 7:4 - Prophets become clearer of mind. Every Christian even new ones have no problem casting out demons. 
• Against Celsus 7:8 - Since the time of Christ there has been no Jewish prophets, only Christian ones. 
• Against Celsus 7:9 - The spirits speaking through the pagan prophets claim to be God, but their speech is "strange, fanatical, and quite unintelligible words, of which no rational person can find the meaning: for so dark are they, as to have no meaning at all; but they give occasion to every fool or impostor to apply them to suit his own purposes."
• Against Celsus 7:10 - True prophets speak the plain truth and some times in parables and enigmas, but spiritual Christian can always figure out the riddles. Satan will counterfeit with riddles that have no real meaning. 
• Against Celsus 7:11- Celsus uses some quotes from Isaiah and Ezekiel to try to prove they spoke unintelligibly.
  

Archelaus (280) writes:

• Acts of Manes 37 ECF 6.179 - The gifts still operate, prophecies, tongues (all the languages of the world) etc.

Ancient Syriac documents:

• Teaching of the Twelve Apostles ECF 7.667 - speaking of the day of Pentecost -- ...according to the tongue every one of them had received, so did he prepare himself to go to that country in which that tongue was spoken.

See also Apostolic constitutions 8.1