I'm not a literalist but from what i understand in my version of Genesis 1 and 2, there is no contradiction. Genesis 2 doesn't actually say that man was created before the animals and plants.
Early in Genesis 2 it says:
'When the Lord God made the Earth and the heavens and no shrub of the field had yet appeared on the Earth and no plant of the field had yet sprung up, for the Lord God had not sent rain on the Earth and there was no man to work the ground. But streams came up from the Earth and watered the whole surface of the ground, the Lord God formed man from the dust of the ground and breathed into his nostrils the breath of life and the man became a living being'
People obviously think that this means man was created at the time described in the first sentence, however there's nothing to suggest this. I think the passage is saying that long ago before animals and plants had been created there was no man to water the ground. Now God is creating man to help water the ground and look after the plants and animals. The passage just misses the part where animals were created, rightly so as this was covered in Genesis 1. Later on it says:
'Now the Lord God had formed out of the ground, all the beasts of the field and all the birds of the air. He brought them to man to see what he would name them.'
Notice that it says 'God had formed', which doesn't imply he created animals at that literal time in the passage, which would have been after man. It merely states that God had formed the animals at an earlier time and now wanted man to name them.
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