There are infinitely many possible shapes. For example an octagon with sides [sequentially] numbered 1 and 5 that are equal.
Another ViewYes the above is true, but specifically a shape with twopairs of congruent, opposite sides is called a parallelogram.
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A parallelogram has two pairs of congruent sides, and the opposite sides are congruent.
A quadrilateral with both pairs of opposite sides congruent is a parallelogram.
Diamond
This is a parallelogram. The first requirement is 2 pairs of congruent sides where the congruent sides are not adjacent. This is like a rectangle (excluding a square) that has two pairs of congruent sides where the congruent sides are not adjacent. But the angles are not all congruent (as set in the question) which pushes the shape into the "next less regular" shape, the parallelogram. The angles will not all be congruent, but it will have 2 pairs of congruent angles. There is no way to avoid the 2 pairs of congruent angles because of the requirement that the shape must have 2 pairs of congruent sides (the first requirement).
2 pairs, the sides opposite each other are congruent to each other