Feeds rich in saturated (SFAs) and monounsaturated fatty acids (MUFA) appear to maximize the retention of long-chain polyunsaturated fatty acids (LC-PUFA) in the fillets of sunshine bass (female white bass Morone chrysops × male striped bass M. saxatilis). To determine whether different sources of SFA and MUFA have equivalent effects on tissue fatty acid (FA) profile change, coconut (CO) and palm oils(PO) were evaluated as partial and complete substitutes for fish oil (FO) in feeds for juvenile sunshine bass. After 8 weeks of culture, the production performance of all groups was within the acceptable range for sunshine bass; however, weight gain was significantly reduced within the 100%-CO group. Partial replacement of FO with CO or PO resulted in significant alteration of fillet FA profiles, and these changes were exacerbated in the complete-FO-replacement groups. The LC-PUFA were disproportionately enriched in the fillets of fish fed the reduced or FO-free feeds, whereas dietary surpluses of 12:0 and 14:0 (CO-based feeds) and 16:0 (PO-based feeds) were not reflected in any of the tissues analyzed. Rather, the levels of the SFA elongation–desaturation products (i.e., 18:0 and 18:1[n-9]) were elevated, particularly within liver lipid, suggesting enhanced FA biotransformation activity among fish fed higher levels of either alternative lipid source. Based on tissue FA composition, PO and CO appear to be approximately equivalent in terms of fillet LC-PUFA retention. However, the digestibility and utilization of these feedstuffs must be further investigated to maximize the ability of PO and CO to (partially or completely) replace FO in sunshine bass feeds.