emission probability using hmmlearn package in python
According to that same documentation you provided, the way to use custom emission probabilities is:

"1.1.3. Implementing HMMs with custom emission probabilities 
If you want to implement other emission probability (e.g. Poisson), you have to implement a new HMM class by inheriting the _BaseHMM and overriding the methods init, _compute_log_likelihood, _set and _get for additional parameters, _initialize_sufficient_statistics, _accumulate_sufficient_statistics and _do_mstep."

NOTE: The documentation pages are for hmm.learn version 0.1.* which is no longer the most recent one. That is, it seems that the documentation page available at any given time might not correspond to the most recent version of hmmlearn. For example, sample code for hmm  0.1.* does not run with hmm learn 0.20.