Well, you've got too little salt in the mobile phase, no salt in the sample solvent when you should have some there, too little organic solvent in the sample solvent, the wrong organic solvent in the sample solvent, and a reequilibration time that's at least 6x too short. Other than that, your method's fine...
To be specific:
1) Reequilibration time:
Separation in HILIC involves partitioning into and out of a semi-immobilized layer of water on the surface of the stationary phase. It takes time to set up this layer. Accordingly, it takes longer to reequilibrate a HILIC column than a reversed-phase or ion-exchange column. Try reequilibrating for 30 minutes.
2) If a sample's viscosity is significantly higher than the viscosity of the mobile phase, then the mobile phase won't mix freely with it but will instead tear off streamers of solvent from the periphery of the sample plug as it migrates down the column. These streamers can migrate through the column faster than the rest of the sample. Result: Multiple peaks for a pure solute. Use ACN in your sample solvent instead of MeOH. The concentration of ACN in the sample solvent should be within 10% of the concentration of ACN in the mobile phase. Here, that would be 70% at a minimum.
3) Your starting mobile phase contains 4 mM ammonium carbonate in 80% ACN. Merck doesn't advertise the fact, but at salt concentrations lower than 20 mM overall, its "zwitterionic" ligands have a net negative charge. Accordingly, under the conditions here, your ZIC-pHILIC is a high-capacity cation-exchange material. Now, note that your various CoA's have charges of (-5), four of these from the phosphates in the CoA nucleotide portion and one from the terminal carboxyl- of your succinyl- or butyryl- adduct. Unless you have enough salt in the sample solvent and in the mobile phase, then such analytes will experience pronounced electrostatic repulsion. Peak splitting is common in such cases, and peak separation to the extent that you've observed is not unusual. You need more salt. You also need to have the same salt in the sample solvent and in the mobile phase. Otherwise, the ionizable groups in the CoA compounds will have a variety of counterions. The resulting ion pairs will differ in polarity and will migrate through a HILIC column at different rates, resulting again in multiple peaks (usually connected by a continuum, reflecting the fact that some molecules swap one counterion for another during their migration through the column).
I'd recommend having at least 20 mM ammonium carbonate overall in the starting mobile phase. You could get that by blending ACN with 100 mM ammonium carbonate online in an 8:2 ratio. However, I'd recommend instead that you pre-mix the solvents so that the mobile phase A reservoir actually contains mobile phase A. Same goes for B. Have the same 20 mM salt in both mobile phases, rather than the gradient from 4-16 mM salt that you're using now. Also, the sample solvent should contain at least 20 mM ammonium carbonate overall.
This combination of electrostatic repulsion and HILIC has a name: ERLIC. Here's a link to a paper that discusses it in detail:
http://pubs.acs.org/doi/pdf/10.1021/ac070997p
Look at Fig. 14 for an extreme case of the problem that you've encountered here. You might be better off with 40 mM salt instead of 20 mM, but first let's get everything else right and then assess the importance of that variable.
I don't suppose that you asked Merck for any technical support for your problem?