In First Samuel chapter 7, the Bible says that the Ark of the Covenant was at Abinadab's house for 20 years:
1 Samuel 7:1-2
1 And the men of Kirjathjearim came, and fetched up the ark of the LORD, and brought it into the house of Abinadab in the hill, and sanctified Eleazar his son to keep the ark of the LORD.
2 And it came to pass, while the ark abode in Kirjathjearim, that the time was long; for it was twenty years: and all the house of Israel lamented after the LORD.
This is prior to Saul becoming king, which happens in 1 Samuel 10:19-25. Saul rules for forty years (Acts 13:21), then David becomes king. It's only after this point that the Ark is retrieved from Abinadab's house:
2 Samuel 6:1-4
1 Again, David gathered together all the chosen men of Israel, thirty thousand.
2 And David arose, and went with all the people that were with him from Baale of Judah, to bring up from thence the ark of God, whose name is called by the name of the LORD of hosts that dwelleth between the cherubims.
3 And they set the ark of God upon a new cart, and brought it out of the house of Abinadab that was in Gibeah: and Uzzah and Ahio, the sons of Abinadab, drave the new cart.
4 And they brought it out of the house of Abinadab which was at Gibeah, accompanying the ark of God: and Ahio went before the ark.
So, does this constitute a contradiction? The Ark was clearly at Abinadab's house for over forty years.
The Ark had been in the possession of the Philistines prior to being returned, and placed in Abinadab's house. This was a period during which the Israelites had lapsed into idolatry, and God was cursing them with persecution at the hands of the Philistines.
The mention of "twenty years" in 1 Samuel 7:2 is simply to mark a turning point in Israel's idolatry, as the passage continues on to say:
1 Samuel 7:1-4
1 And the men of Kirjathjearim came, and fetched up the ark of the LORD, and brought it into the house of Abinadab in the hill, and sanctified Eleazar his son to keep the ark of the LORD.
2 And it came to pass, while the ark abode in Kirjathjearim, that the time was long; for it was twenty years: and all the house of Israel lamented after the LORD.
3 And Samuel spake unto all the house of Israel, saying, If ye do return unto the LORD with all your hearts, then put away the strange gods and Ashtaroth from among you, and prepare your hearts unto the LORD, and serve him only: and he will deliver you out of the hand of the Philistines.
4 Then the children of Israel did put away Baalim and Ashtaroth, and served the LORD only.
So, the twenty years did not set an upper limit on the amount of time the Ark was at Abinadab's house. Rather, it is stating that it was twenty years after the Ark was moved to his house that Israel finally ceased to worship other gods.
Also, the account in 1 Samuel 7 never says "and after twenty years, it was removed". It says it was there for 20 years. This statement would be true if it remained for 40, 400, or 4,000 years, because 20 is a subset of all of those numbers. Therefore, even if the account did not include the detail about Israel's idolatry, this wouldn't constitute a contradiction.