What was inside the Ark of the Covenant? 1 Kings 8:9 (NIV) There was nothing in the ark except the
  two stone tablets that Moses had placed in it at Horeb, where the Lord made a covenant with the Israelites after they came out of
  Egypt.
  
  Hebrews 9:3-4 (NIV) Behind the second curtain was a room called the
  Most Holy Place, which had the golden altar of incense and the
  gold-covered ark of the covenant. This ark contained the gold
  jar of manna, Aaron’s staff that had budded, and the
  stone tablets of the covenant.


1 Kings 8:9 says that inside the Ark of the Covenant there was only the two stone tablets of Moses. But Hebrews 9:3-4 mentions three things, the gold jar of manna, Aaron’s staff that had budded, and the stone tablets of the covenant.

Keeping in mind that the Ark of the Covenant was no more during the time of Jesus, the writer of Hebrews simply recalled from the Torah or from tradition about the contents of the Ark. In fact, even the writer never saw the Ark with his own eyes, let alone what was inside.

Regarding the pot of manna,


  Exodus 16:33-34 (KJV) And Moses said unto Aaron, Take a pot, and put
  an omer full of manna therein, and lay it up before the Lord, to
  be kept for your generations. As the Lord commanded Moses, so Aaron
  laid it up before the Testimony, to be kept.


This verse only says "before the Lord/Testimony" and not inside the Ark. 

Regarding the staff of Aaron,


  Numbers 17:10 (NIV) The Lord said to Moses, “Put back Aaron’s staff
  in front of the ark of the covenant law, to be kept as a sign to the rebellious. This will put an end to their grumbling against me, so
  that they will not die.”


This verse also says that the staff of Aaron was placed in front of the Ark. 

Questions:


Do these verses from the Old Testament contradict the Epistle to the Hebrews? 
What exactly was kept inside the Ark of the Covenant?
In his commentary on Hebrews 9:4, John Gill notes,


  but how this pot, as well as Aaron's rod, can be said to be in the ark, when it is asserted, at the bringing of the ark into the temple, at the dedication of it by Solomon, that there was nothing in it but two tables of stone, (1 Kings 8:9; 2 Chr. 5:10) and both the pot of "manna," and Aaron's rod, are said to be before the testimony, (Exo. 16:34; Num. 17:10) and not in it, is a difficulty.


John Gill supposes that


  the preposition ἐν sometimes signifies "at," or "with," as in (Col. 3:1; John 1:28; Eph. 6:2) and so the sense is, that these were near unto it in the most holy place, and might be in the sides of it, though not within it; for there were places in the sides of the ark to put things into (Deut. 31:26; 1 Sam. 6:8) .


In 1 Sam. 6:8, the author writes that "vessels of gold" (כְּלֵי הַזָּהָב) were placed beside it (the Ark) (מִצִּדּוֹ). These vessels of God were "five golden hemorrhoids and five golden mice" (cp. 1 Sam. 6:4). We know without a doubt that the scriptures never mention any of these being present in the Ark itself. So, we may assume that there was some sort of storage space beside the Ark, yet the exact nature of this storage is unknown. Another possibility is that makeshift platforms were placed beside the Ark at various times to hold such things. Again, scripture is not clear.

Yet, one thing seems to be clear, and that is that there was nothing in the Ark except the two tables upon which were written the Ten Commandments (cp. 1 Kings 8:9). I would tend to agree with Gill's assertion that the Greek preposition ἐν can mean "with" (it is so translated in the A.V. 140 times). There are many examples of ἐν followed by a relative pronoun being translated as "with" (e.g., Matt. 7:2; Rev. 19:20).

Even if the pot of manna and Aharon's bud were located by the side of the Ark, they would still be considered "in the presence of YHVH" (לִפְנֵי יְהוָה; cp. Exo. 16:33) because YHVH dwelt between the kruvim (cp. 1 Sam. 4:4).

One more point to note. In Num. 17:7, it is written that Aharon's rod was to be brought "before the testimony"  or "in the presence of the testimony" (לִפְנֵי הָעֵדוּת). Some might assume that the "testimony" (or "witness) referred to here is the two tablets of the Ten Commandments (cp. Exo. 25:16). Thus, they may conclude that the rod and the pot of manna had to be in the immediate presence of the tablets contained inside the Ark itself. However, in his commentary on Exo. 16:34, Avraham ibn Ezra writes,


  לפני העדות שהוא הארון. ונקרא ארון העדות בעבור לוחות הברית שהיו שם


which is translated as,


  "Before the testimony," which is the Ark. And it was called "the Ark of the testimony" (cp. Exo. 25:22) on account of the tablets of the covenant that were there."


In summary, it's possible that there is no contradiction and that instead of being "in the Ark," the pot of manna and Aharon's rod were "with the Ark" inside the Temple and/ or Tabernacle.