Expecting anyone to believe this is asking too much.
Literal
This [object-を] believe[quotative-って] side [subject-が] impossible [copula-だな].
信じろって方が無理 'it's the believing side that's unreasonable' — a sharp rhetorical reversal. ~って方が 'the one who says...' frames the demand as the unreasonable party. 無理 'impossible, unreasonable.' だな is masculine reflective. A pithy dismissal.