An anti-Laplacian prior is defined in the obvious way; if you've observed R red balls and W white balls, assign probability (W + 1) / (R + W + 2) of seeing a red ball on the next round.

An anti-Occamian prior is more difficult, for essentially the reasons Unknown states; but let's not forget that, in real life, Occam priors are technically uncomputable because you can't consider all possible simple computations. So if you only consider a finite number of possibilities, you can have an improper prior that assigns greater probability to more complex explanations, and then normalize with whatever explanations you're actually considering.