Two dental implants costs thousands of dollars. Can I ask the dentist to accept half cash payment and make 2 other payments the second half of the yr.

Never hurts. to ask. What's the worst they tell you-- no? doctors are small businesses-- each does what makes sense for their business and most, if they are smart, are willing to make arrangements to maintain happy patients!
Every office. Every office has an internal protocol for extended payments. Know that by asking the Dentist for extended terms, you are asking for a discount, you are asking the Dentist to finance your treatment, probably at no interest. Know that the implant manufacturer, dental lab, electric company, etc, are not helping the Dentist finance your treatment.
You can ask. And then you will know if this is acceptable to your provider.
Yes, you can ask. If you're paying for your dental services on your own, don't overlook the option of making some type of financial arrangement directly with your dentist. Most of the dentists will frequently have some type financing plan (no interest) to offer to their patients. Good luck.
Third party payments. Perhaps your dentist would be interested in participating in third party healthcare programs, such as carecredit or lending tree. The dentist is paid up front and the patient can work out the terms usually between three and twenty-four months and many times this is interest free to the patient as the dentist absorbs the percentage off.