Contradiction with James 1:5
While Psalms 59:10 speaks of God's mercy, James 1:5 emphasizes God's role in providing wisdom to those who ask, which may seem like a different aspect of God rather than a contradiction.
James 1:5: If any of you lack wisdom, let him ask of God, that giveth to all [men] liberally, and upbraideth not; and it shall be given him.
Contradiction with Proverbs 15:29
Psalms 59:10 speaks of God's mercy as close to the righteous, while Proverbs 15:29 suggests God is far from the wicked, which might imply a conditional nature to God's responses rather than a pure contradiction.
Proverbs 15:29: The LORD [is] far from the wicked: but he heareth the prayer of the righteous.
Contradiction with Lamentations 3:32-33
While Psalms 59:10 talks about God in the context of steadfast mercy, Lamentations suggests He can cause grief, which is seemingly at odds with a purely merciful view.
Lamentations 3:32-33: But though he cause grief, yet will he have compassion according to the multitude of his mercies.