Making bivariate colour ramp with QGIS?

Excellent answer by @Martin but it seems you have 2 attributes you want to have a colour gradient (Plantation Cover and Forest Harvesting Intensity). If I'm mistaken then I will remove this post. You could set up a Rule-based style, create a new rule, edit the symbol layer from a Simple Fill to a Gradient Fill. Create a filter for your attribute column and set your colours. Then repeat by adding another style rule:

In QGIS 2.6 you can create a two color color ramp this way:

Double click on the layer (or right click > Properties) > Style > Change from "Single Symbol" to "Categroized" > Color Ramp > Random colors> Select Gradient > Choose the colors and safe > Choose the column with the values > Classify > Apply

In the "Column" field you have to select the column containing the values that should be displayed in the color ramp.