Were Jewish, Greek, and Gentile converts adults only?
Answer: 1) Yes, and 2) not quite.
Since young children are incapable of understanding repentance, they cannot be converted until they reach an age where they qualify. This is often considered the age of accountability, somewhere around 13 or older.
When the text states that one's entire household was converted, it cannot mean very young children because they possess little or no knowledge of the concepts necessary for salvation.
Previous mention has been made of the salvation attained in both Lydia's household as well as the Philippian jailor's. In both instances, note the central role of baptism, a biblical imperative. These early converts were baptized in their respective households "immediately."
However, it goes without saying that tiny children could never submit to this rite. They have very little concept of right and wrong, let alone good and evil.
It should be apparent to all that the specifics pertaining to redemption should be the easiest of all subjects to grasp in Scripture, and that is certainly true. As one preacher on the radio often suggests: "The main things are the plain things, and the plain things are the main things."
Author and commentator, Wayne Jackson of The Christian Courier wrote of such ideas, in this instance the debate over infant and child baptism:
It is suggested [that] baptism was symbolically pictured by circumcision. Colossians 2:11-12 is employed as a proof-text for this position. Since circumcision was for infants, it is contended that baptism is similarly for infants today.
There are several major flaws in this argument: 1) If circumcision typifies baptism, in the sense argued by pedo-baptists, then only males should receive baptism because only males were circumcised; 2) the only analogy between circumcision and baptism, as per Colossians 2:11-12, has to do with the fact that both involved “putting off the flesh.”
Circumcision [literally] severs the flesh. But in baptism, one determines to sever himself from fleshly pursuits. That exhausts the connection between circumcision and baptism. [Finally], since baptism is “for the remission of sins” (Acts 2:38), it is not appropriate for infants or young children, because they have no sin (Matt. 18:3; 1 Cor. 14:20) [even if they ever understood what "remission of sins" meant].
No doubt many will argue that we are born sinful. I will not take the time to address that concern in this response.
The takeaway from this discussion is that child conversion is foreign to the New Testament. The redemption of infants and young children was never established either by Christ or His apostles. We must, therefore, conclude that when one speaks of a "conversion," as is the case with Acts 16 and many others:
The converts were all adults (whether younger, or older).
 Alistair Begg is the senior pastor of Cleveland's Parkside Church in Ohio.