The 1841 British edition omitted the first subordinate that in this passage, but the subsequent 1849 LDS edition restored it. Note here that we have a conjoining of two complete that-clauses (“that there is no God or that Christ cometh not”). It turns out that there are examples in the original text like the secondary 1841 conjoining, as in the previous verse where there is no that for the first conjunct: “I know there is a God and also that Christ shall come” (Alma 30:39). In fact, it is possible that here in verse 40 the 1841 compositor was influenced by the language of the previous verse. For further discussion on the optionality of the subordinate conjunction that, see under that in volume 3 .
Summary: Maintain both occurrences of the subordinate that in Alma 30:40 (“and now what evidence have ye that there is no God or that Christ cometh not”).