AS soon as you ask if you can carry a gun in their store, you will be looking for a new store.
With owners/managers you are unsure about, try to think creatively about your approach. When it's less of a "question" and more of a mere "confirmation", incident to doing business with them, owners/managers may be more inclined to just "go with the flow". Example (the scenario is you are on the phone, because usually if you are asking permission beforehand it means you can't step foot on the property without it):
(Record the phone conversation. Yes, it is legal to do so in Michigan without informing the other party as long as you are a party to the conversation.)
Just the direct question:
You: "May I carry my gun in your business?"
Owner/Manager: "No." (The usual response by an unsure person to an "unusual" question they've probably never had to answer before.)
Perhaps a more successful approach:
You: "Hi, this is Dan M. [be sure to state your name] . . . [Discuss what you're looking for, if their business provides it, they have something in stock, prices, etc. . . .
establish in their mind that you are a potential customer.]
Owner/Manager: [Discusses with you what you are looking for.]
You: Great! I think you have EXACTLY what I'm looking for. [If possible and appropriate, get them to hold an item for you, make an appointment for you, or whatever other thing can cause
a psychological commitment in their mind to accepting you in their business.]
Owner/Manager: Glad you called. Sure we'll [hold that item in stock, make an appointment, etc.] for you!
You: Oh, by the way, I carry a gun in accordance with the law and all the businesses I frequent are OK with lawful carry. Since you happen to have a liquor license, I
technically have to ask your permission to carry on your property. Are you OK with that while I [insert the business you are potentially going to do with them]?
Owner/Manager: Sure, I'm fine with that.
I think the second approach is more probable to be successful, since you've set up in the owner/manager's mind that you are a customer wanting to do business, other businesses don't have a problem with your carry, and the permission to carry is just a mere technicality in the law, which is what it really is. Most people just "go with the flow", and sometimes it is helpful to psychologically guide folks into the "flow".