/s/ + /r/
/s'/ + /r/
/s/ + /r'/
/s’/ + /r'/


/r/ + /s/
/r'/ + /s/
/r/ + /s'/
/r’/ + /s'/

Does anyone know the results of these two coming together?

/s/+/r/, /r/+/s/ - nothing special really happens.

The other depends if it is beginning of the word. Have to look closer at the rhing

/r'/+/s'/=/rs'/ - this one I know for sure. Like in "doirse"

/sr/, /rs/ are often pronounced with a velarised "sh" sound, i.e. not the one that's a common Irish "sh" (as in sean, for example), which is palatalised and, thus, sounds lighter. This thing (/sr/, /rs/ > /∫r/, /r∫/) happens in Connemara Irish. Thus words like srian, sruth, sráid have parallel forms with the initial /∫r/ or /sr/ cluster.
In the case of /r/, /r'/ + /s'/ colliding at the word boundry (like an fear seo), the same rule holds true, and /s'/ becomes "darker". As far as I can tell, the "r"-sound in the clusters /∫r/, /r∫/ is a /r/ of the Queen's English (the so called retroflex approximant). It seems to me it has developed in this position all by itself with no external influence whatsoever.

So, drawing a conclusion:

/s/ + /r/ = /sr/, /∫r/ (e.g. srian, I have no word-internal examples)
/s'/ + /r/ ?
/s/ + /r'/ ?
/s’/ + /r'/ ?


/r/ + /s/ = /rs/, /r∫/ (e.g. fearsaid)
/r'/ + /s'/ (through the stage of the depalatalised /r'/ of course)= /rs/, /r∫/ (e.g. fairsing, the /rs'/ varient seems by far more common in Connemara, though /rs/ is not turned down altogether; /rs/ is typical of Donegal (? tursach) as far as I can see)
/r/ + /s'/ = /r∫/ (as well as in the all exx. above: relroflex "r", velarised "sh")
/r’/ + /s/ ? (following the logic it must be /rs/, but as long as this sort of cluster can be found only at the word boundary, the rule may fail; an obair san iothlainn /rs/ or /r's/ ??)