Abarim Publications' online Biblical Greek Dictionary
The noun κοιλια (koilia) broadly refers to the lower part of a mammal's main body. It comes from the noun κοιλος (koilos), meaning hollow, which was used as broadly as to refer to the hold of a ship, a valley or a natural harbor, with the connotation of being empty. That indicates that our word mostly emphasizes the thorax as a big hollow vessel.
Our noun κοιλια (koilia) may denote the entire thorax, including the lungs, but mostly emphasizes the belly — stomach and bowls — and as such was mostly associated with the intake and digestion of food (and expelling of wastes). The κοιλια (koilia) also served as the seat of emotions, often juxtaposed with the καρδια (kardia), heart, or the seat of one's conscious thoughts (Matthew 12:40, Mark 7:19).
Most strikingly, both our noun κοιλια (koilia) and the noun γαστηρ (gaster; see below) are frequently deployed to mean womb. This seems to suggest that the gestation of a child in one's womb was mostly associated with emotional or subconscious construction rather than intellectual construction (see the noun τεκνον, teknon, child).
It also demonstrates that to the Greeks, physical pregnancy was a mere physical manifestation of a kind of process that all humans are intimately familiar with. The word that was specifically reserved for womb is μητρα (metra), from μητηρ (meter), mother, and that word is used only twice in the New Testament. Our noun κοιλια (koilia) occurs 23 times (see full concordance) and 12 times it is used to refer to a pregnant belly (that is: a hollow utilized).
The noun γαστηρ (gaster) also refers to the digestive tract, and specifically the stomach, but rather emphasizes the desire for filling it with food (hence our word gastronomy). Greek words for gluttony and "belly-slave" all derive from this noun.
And as with κοιλια (koilia), our noun γαστηρ (gaster) is frequently deployed to describe one's womb, which in turn emphasizes the desire of a woman for a child (and thus for a husband). Our noun is used 9 times (see full concordance), and 8 times it refers to a pregnant stomach (that is: a desire fulfilled).