Yeah, the 2 main ways to form the causative in Irish are, as far as I know:

tabhairt ar dhuine rud a dhéanamh
and
duine a chur ag déanamh ruda

(Thug mé ar Sheán an t-urlár a ghlanadh & Chuir mé Seán ag glanadh an urláir)

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

In Irish English the phrasing would be to put Sean (onto) cleaning the floor or to put him onto the floor so maybe cuirfead Uilliam (ag obair) ar an gcarr captures the same idea



I'll put Mary (to) finishing the reports
I'll put Mary to the finishing of the reports
I'll tell Mary to finish the reports

I'll have Mary finish the reports sounds like a promise to instruct or even ask her a little bit later and to be done within an expected, normal timeframe, so one and two above might be nearest

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

Go raibh maith ag chuile dhuine! Very helpful!

They may not be direct translations but this is how I'd say them.

I'll have Mary finish the reports.
Iarrfaidh mé ar Mhary na tuarscáil a chríochnú. (I will ask..)
or
Dearfaidh mé le Mary na tuarscáil a chríochnú (I will tell...)

I'll make John clean the room.
Cuirfidh mé iallach ar John an seomra a ghlanadh.

Water makes the grass grow.
Cuireann uisce an féar ag fás.