There are several tools for dealing with presence-only data (MAxEnt, MaxLike etc). Using occupancy you can incorporate and model the uncertainty of false negatives (False absences). The use of a markovian dependence models depends on how the data is collected. I guess what you mean (tiger on trails (2010) and a paper from 2011 in J. Anim. Ecol) but the neccesity of using the MArkovian dependence is due to the sampling methodology . The field sampling from this papers lacks independence between neigbour spatial replicates over the survey, and thus it should be modelled.
Of course you can integrate different sources of data into occupancy modelling
Or you can use library "unmarked" within R or bayesian approaches with Bugs or jags also within R.
You just need to see which kind of data you have and which constrains you need, and then see if it is implemented in Presence or unmarked or try to implement it with Bugs or jags
What kind of data do you have? The standard site-occupancy model is a non-spatial model. Maybe you can use a spatial autocorrelation model (http://rstudio-pubs-static.s3.amazonaws.com/9688_a49c681fab974bbca889e3eae9fbb837.html) or a spatial capture-recapture model with camera trap.