Unfortunately, you definitely won't find a birth cert for Ann since Civil Registration of births only commenced in Ireland in Jan 1864 - your only hope, therefore, is a baptism record.
On ancestry.com, there is the following record for John Wright:
Ireland, Tithe Applotment Books, 1823-1837
Name: John Wright
Year: 1833 & 1834
This might give you a parish to search for Ann or Samuel's baptisms.
On Griffiths Valuation Ireland http://www.askaboutireland.ie/griffith-valuation
there is a Samuel Wright living in Castledermot, Co. Kildare. Lots of other Wright's there too.
I had a look for you on IFHF/RootsIreland (pay) site for a baptism for either Ann or Samuel, but no luck; however, there are 5 baptisms in Kildare between 1821-1829 for children with father John Wright & mother M (specifying Martha didn't give any results, but just putting the initial M did). Don't know if this is of any help.
If their father worked for the Army, perhaps he moved around, and Ann & Samuel were born somewhere else?
Anyway, happy hunting!