Karen, the index you looked at in SLC was probably the IGI which is online at FamilySearch.org. Or see:
www.familysearch.org/eng/search/frameset_search.asp?PAGE=igi/search_IGI.asp&clear_form=true

This has JAMES CALLISTER Christening: 18 SEP 1842 Patrick, Isle Of Man, Father: WM CALLISTER, Mother: MARTHA KERMEEN.
This is an extracted record (from the parish register). The Source Call No. is given at the bottom of the screen - LDS film no. 0106738.

A second extracted entry gives the same details with the place as Dalby (same film number).
On the same film is a marriage in Patrick between William Callister & Margaret Kermeen (extracted record), but the date is 11 Nov. 1837 which seems too late - see the bapts below. And Margaret rather than Martha. There is another marriage record for the same couple that year, but it is a member's entry (unreliable).

You can photocopy any of the entries from this film at SLC or at your local LDS Family History Centre. The film, as Frances wrote, is the 1911 copy of the original register, and the extracted records are very good.

Earlier extracted records for their probable children show Edward, John, and Jane bapt in Onchan in 1836, 1834, and 1832 (mother Martha but her surname not given). LDS film no. 0106715.

The only marriage between James Callister and Elizabeth CORLETT that I could find around the date you gave was on 11 JAN 1868 Ballaugh, Isle Of Man (extracted record).
The LDS film no. is 0106178.
On the same film is the bapt of their daughter Ada Elizabeth Callister, on 3 Feb.1868 Ballaugh.

Mona Belle Callister's birth was registered on 24 Mar 1887 Ballaugh, father CALLISTER, James, mother CORLETT, Elizabeth.
From www.iomfhs.im/lawsons/births/callister.html

You can buy this cert from the Registry. See "Contacts" www.gov.im/registries/general/civilregistry/

Sue