Dont know if you have these already, but will include just in case not...
Marriage of Robert Monk and Bridget Field - 1822
Their children include - Alice 1823, Catherine 1825, Ann 1828, Mary Anne 1830, and Patrick 1840
(all Rush RC)
Have you seen an image of the original baptism for your Richard - e.g. on microfilm ?
His father's name is matching John for me on RootsIreland searches - the other details match ok, parish, surnames and mother's first name.
Based on Griffth's valuation it look like your Robert may have held a house and Garden and several small plots of land in Rush townland, all leased from Sir. Robert Palmer who appears as a landlord frequently for this area. One of the entries dated 1847 shows a Robert Monks occupying a house and garden, on part of plot number 170. The location seems to be between the Whitestown and Channel roads just west of the town, see : here (1st edition OSI map c1837 so a little earlier than the date for that Griffith's).
You can search the Valuations on the LibraryIreland website on AskAboutIreland, the site includes transcripts, images of the published valuation books and maps with plot number, although the version they use date from later than the valuation, so dont always match the plot numbers used.