Let's cultivate through experience the sensibility needed to make a marriage work!
Literal
Married-couple-between [subject-が] well-going [for-ための] sense [object-を], experience [by-によって] cultivate-[progressive-ていこう]!
夫婦間 ('between spouses') sets the relational scope. うまくいくための ('needed for things to go well') is a purpose clause. センス is the loan 'sense/sensibility.' 養っていこう uses the volitional of ~ていく ('let's continue to cultivate going forward'). The exclamation mark gives it a self-help motivational tone.