Inverse Problem / Deconvolution with Pink Noise
Some Remarks:


2nd Order Knowledge
It seems you only have a knowledge about the Auto Correlation of your data (2nd Order) and not on its distribution. Hence methods you can apply are ones which minimizes only 2nd order functions of the noise (Such as MMSE).
Wiener Filter Minimizes the MMSE
As can be seen in the derivation of the Wiener Deconvolution Filter the only assumption made is independence from the signal. If that holds in your data this is a good solution. Pay attention that Wiener Filter model is that the input data is also stochastic and all data is wide sense stationary.
Richardson Lucy Deconvolution
Pay attention this is a Maximum Likelihood method. Namely it assumes the data is a parameter, not a random data. It also assumes the distribution of the noise and not only its second moment,
Decide the Cost Function
First thing you should decide what would you like to minimize according to your model. Does the MMSE makes sense? Maybe a Least Squares is good enough? May you come with other objective. This is the first step.