The Idea in Brief
The New Testament is explicit that women do not hold the "office" of teaching (or pastoring), but they may nonetheless have the "gift" of teaching. In the case of the "office" of deacon, there is no explicit expectation or reference that such people need teach the Word of God (as is otherwise the case with the overseer in the same context); therefore women appear qualified to hold this "office," especially in light of two passages in the Christian New Testament that indicate women were hosting local church meetings in their own homes.
The "office" of teaching appears to be exclusive to men in the Christian New Testament (1 Cor 14:34 and 1 Tim 2:12), however the "gift" of teaching does apply to women, who may be teachers in the local congregation.
Titus 2:3-5 (NASB)
3 Older women likewise are to be reverent in their behavior, not malicious gossips nor enslaved to much wine, teaching what is good, 4 so that they may encourage the young women to love their husbands, to love their children, 5 to be sensible, pure, workers at home, kind, being subject to their own husbands, so that the word of God will not be dishonored.
That is, such women hold no "office" of teaching, but they nonetheless have the "gift" of teaching.
There are also two examples in the Christian New Testament where women appear to be hosting the local church in their homes, and so they appear to hold the "office" of deaconess, because they appears as servants (= διάκονος in Greek).
Colossians 4:15 (NASB)
15 Greet the brethren who are in Laodicea and also Nympha and the church that is in her house.
2 John 1:1 (NASB)
1 The elder to the chosen lady and her children, whom I love in truth; and not only I, but also all who know the truth,
The women in the above two verses appear to be servants (deaconesses) because the passage of 1 Tim 3:8-13, which discusses this "office," makes no mention concerning the exercise of authority (as is the case of the "office" of overseer in 1 Tim 3:2, who must be able to teach). The context at hand provides more insight in this regard.
1 Tim 3:11-12 (NASB)
11 Women must likewise be dignified, not malicious gossips, but temperate, faithful in all things. 12 Deacons must be husbands of only one wife, and good managers of their children and their own households.
The same Greek word for "woman" in the above verse (in regard to the "office" of deacon) is the same word used for "woman" in the verse below (in regard to the "office" of teaching) in the same epistle.
1 Tim 2:12 (NASB)
12 But I do not allow a woman to teach or exercise authority over a man, but to remain quiet.
In other words, the "office" of deacon may be held by women, but there is no expectation that such persons --whether men or women-- teach anyone as would otherwise be the case of the overseer (or even the pastor), who is male, and who is expected to teach as part of their "office." Again, the exclusion of women from the "office" of teaching does NOT imply that they do not have the "gift" of teaching.