The Skeptic's Annotated Bible lists seven verses related to the contradiction. Five against coveting and two supposedly for coveting.
Against:
Exodus 20:17 & Deuteronomy 5:21- The word for covet here is ṯaḥ·mōḏ (תַחְמֹ֖ד). This word is used in Exodus twice, once each in Deuteronomy 5:21 & 7:25 and in Proverbs 6:25. The first three uses are in the Ten Commandments. In Deuteronomy 7, Moses is telling the people what they should do when they enter the Promised Land. That prohibition is related to the gold and silver on the pagan idols they will encounter. They are not to covet the metal or take it. Proverbs 6 warns against desiring an adultress. In the Septuagint the word is epithymēseis (ἐπιθυμήσεις) which is exactly the word Paul uses in...
Romans 13:9 - Paul is quoting the Ten Commandments using the Greek translation of the Hebrew Old Testament, the Septuagint. Epithymēseis is a form of epithumeó which occurs in various forms sixteen times in the New Testament. Some uses are positive, e.g. Matthew 13:17 and Luke 22:15 and some are negative, e.g. Matthew 5:28 and James 4:2. It's pretty easy to see the differences in the positive and negative uses from the context of their respective passages.
Ephesians 5:3 - The word here is pleonexia (πλεονεξία) which occurs in forms ten times in the Bible. Pleonektés, which is used in Ephesians 5:5 is the root word of pleonexia. All of these occurrences are negative in connotation.
Colossians 3:5 - The word for covetousness is a form of pleonexia as in Ephesians 5:3.
For:
1 Corinthians 12:31 - Here the word is zēloute (ζηλοῦτε) from which we get our words zealous and jealous. This is the exact word used in...
1 Corinthians 14:39 - Forms of zéloó (the root of zēloute) are used twelve times in the Bible. In Acts they are negative, in the letters to the Corinthians they are positive, in Galatians one is positive and one negative, James' use is negative, and John's use in Revelation is positive.
In all the cases above, it is clear from context what is being affirmed or prohibited. Desire after the things of God is good. Desire for earthly things or dissatisfaction with what you have, i.e. what God has given you, is bad.
So this "contradiction" boils down to the skeptic saying, "Look the same word was used in two different ways, let's forget context and chalk up another contradiction so the number of contradictions we've found is even bigger."
The interesting thing to me is that, in ignoring context and only focusing on one translation (KJV), they missed the fact that the Tenth Commandment listed in Exodus uses the same Hebrew word for covet both times in the verse and when it is reiterated in Deuteronomy only the first use is the same word as in Exodus. The second is a different word (ṯiṯ·’aw·weh/תִתְאַוֶּ֜ה). That seems more like an actual contradiction than the grasping at straws type of "contradiction" they list. It also warrants more study to find out why the two verses differ when one would assume Deuteronomy should be an exact copy of Exodus.
Note: I am not a fan of Blogger's formatting of this post, but I barely had time to right write (update 2018-02-10) this post much less typeset it.