When you first start using the services offered by a local courier service one of the first things you will wish to discuss with them is the method by which they like to get paid. For many people running a business, the majority of the expenses are simply applied to the company credit card and then paid off monthly. There are a lot of courier services, a majority in fact, that will accept credit cards as your primary form of payment, so you should have no problem using a card to pay your account with your courier company normally.
However, if your business is willing to use a different courier service that doesn't take credit cards, you shouldn't worry that it is a sign of bad business on their part that they don't. Many of the most successful companies in any field don't accept credit cards simply because they don't want to deal with the hassle of having to include that aspect in their operations and their accounting practices. It is by no means an indicator of a company that is going to provide anything worse in terms of the actual service that they offer simply because they do or do not accept credit cards. If anything, this should only influence your decision as to which company to do business with based on your own companies preferred methods of dealing with the accounts you must pay monthly.
Finally, if the particular courier service that you do business with does accept credit cards, be sure to investigate the types of cards that they accept. If you use a card that is not one of the big three, Visa, MasterCard, American Express, than there is a chance that the company might not accept your particular kind of card. This could create difficulties for you when the time comes to pay your account, so if you're just starting to do business with a new courier company, simply take a minute to sit down and discuss the payment options that they offer and prefer before finalizing any arrangements. It will usually only take a minute to have this kind of a discussion but it can avoid awkward situations further down the road if there is a conflict of any kind in terms of the payment methods accepted. Any company is going to totally upfront with you about what they accept, and any fees that might be associated with a given method of payment, so simply discuss it before your first payment comes due.