There is no such thing a constructive conflict from the get-go, but on the other hand, there are conflicts that become constructive.
For example, let's say two developers are having a conflict about which PHP framework to use in a software development project. Everyone is pushing for the framework he's used to, but eventually, they both discover that both of their frameworks are buggy and do not work best for the project. So, they end up choosing a 3rd framework that is much more stable and ideal for the project. In this situation, a conflict (that is normally negative) generated a positive (constructive) outcome, which was for the benefit for the project.
Let me give you another example, let's say the project manager is having a conflict with the supplier: the PM is accusing the latter of pricing the material higher than the market. The supplier does not concede to the accusations so the project manager seeks another supplier, and finds one that provides the same material at a much cheaper price. Obviously, the conflict resulted in saving money for the project, and so it became a constructive conflict.