If you want a very strong absorption then I suggest to use a metamaterial, in particular a so-called "Perfect Absorber". It can be tuned exactly to 1064 nm and to have an absorption of virtually 1 (which means that reflection and transmission are both zero). See e.g.
How spectrally selective does it need to be? How much power does it need to handle? Is the source collimated?
If the answers are No, 100 mW or less, and Not really, then a piece of silicon or germanium might do nicely.
Other things to consider - what absorption efficiency do you need? Is absorption required, or would high reflectance suffice? Perhaps an interference filter could be applicable.