On the Acts of the Apostles

παις  is from  παιω which means "to hit, not very violently, one time."   παις is used 24 times in the New Testament and 6 times in the book of Acts.  It has a variety of meanings.  According to Strong's concordance (word number 3816) it is used 10 times as servant; 3 times as son; 7 as child; 2 as maiden; 1 time as manservant; and 1 time as a young man.  The main meanings are that of a child and that of a favored servant.  Both meaning are valid.  In ancient Greece it was usually used to be an honored servant.  We know it can also mean son, because in John 14:46-51, the same person is described by both υἱος and παιδιον.  We know that υἱος means son, so παιδιον must be able to mean son.  And παιδιον is used in the same way as παις in several places.  King Context, common sense, and prayer are the main deciders of meaning.  

Acts 3:26 has some controversy over whether it should read as Son or servant.  "To you God first raised up His 'παιδα,' Jesus." Calvin and Jamieson in their commentaries both make the point that it should be translated servant, yet the context has just been talking about children, fathers, and the seed through which all will be blessed - indicating that it should be translated son.   I think this is a situation where either one will do - but stick a footnote their, just to make sure it's clear.

An interesting moot point is that in Islam it is always translated servant, and they tend to use that as one of their proofs that Jesus was not, in fact, God's son, but merely His servant and messenger.