It depends on what it is, look at what your device is in the table:

Verification
Verification is the easiest and quickest authorization route.
Verification just involves you sending your product and any required
auxiliary equipment and cables to a test lab. The lab spends
approximately 1-2 days measuring the radiated and conducted (if
required) emissions coming from your product. If all is well, they
generate a test report and send it to you. That’s all there is to it.
You’re now at liberty to label, market and sell your product.
Of the 1000 or so FCC test labs around the world, you can select any
of them to do this job. From the FCC’s perspective, there are “2.948
listed” test labs and “accredited and FCC recognized” test labs. The
difference is that trusted independent 3rd party companies are used to
inspect accredited labs to verify a certain level of competence and
that procedures are implemented and being followed properly. For
non-accredited, registered test labs, no such 3rd party inspection
take place. Approximately 2/3 of FCC test labs around the world are
not accredited.
Declaration of Conformity (DoC)
Not to be confused with the Declaration of Conformity for Europe,
which is completely non-related, the DoC method for the FCC covers
certain types of electronic equipment.
If your device is in a category that allows the DoC authorization
route, the key here is that you need to select an FCC accredited test
lab. Test labs that are only ‘2.948 listed’ with the FCC and are not
accredited, are not allowed to test devices using the declaration of
conformity authorization route.
Before these new rules, “Listed” (or non-accredited) test labs could
get around this requirement by instead undertaking ‘certification’
testing on your device. But that option will no longer be available to
you or to the test lab when the rules come into full effect. So,
products subject to the ‘DoC’ authorization route will only be able to
be tested at an accredited lab.
Certification
Certification testing requires an application package of test results
plus other documentation be sent to a special test lab called a
Telecommunication Certification Body (TCB). Both accredited and
non-accredited test labs could previously do the testing for
certifications. After these rules come into effect, only accredited
labs will be able to perform the testing. It’s worth noting that TCBs
can also perform the testing themselves as well as issue the
certifications.
Source: EMC fastpass
Are we required to use an accredited lab for the Class B unintentional
measurements?
Ultimately, my company's you know what, is on the line as the
certifying party. So why can't we take the readings, and certify?
If the product being tested only needs verification, then you could test at a lab that has been registered with the FCC. If you need a DOC, then you'll need to go to an accredited lab.
Of course, you can always test in your lab before you send the product out for testing to make sure the testing goes smoothly and you don't have to do a second round.
The only place I read that the Class B DoCs must come from accredited
labs, are from the websites of accredited labs!
No, the FCC also tells you that you need DOC's from an accredited lab:
Q: I don’t have the expertise in house at my organization. Who can
provide FCC equipment authorization?
A: Unless you are fortunate
enough to have an accredited in-house FCC laboratory in your company,
the best choice is to involve a third-party FCC lab at the design
stage and then follow through with testing of your product at the lab.
Q: Is one lab as good as another?
A: There are many EMC labs around the world. In accordance with 47 CFR
2.948, the FCC list labs that the FCC has on file for FCC Verification
equipment authorization. For any FCC work, your lab should be on this list.
Furthermore, if the device requires Declaration of Conformity
equipment authorization, the lab must be ISO/IEC 17025 Accredited. An
accredited lab has been audited by a third party such as the American
Association for Laboratory Accreditation to the international standard
for good laboratory practice ISO/IEC 17025.
The following website: http://www.fcc.gov/oet/ can be used to find an
FCC lab that is listed under 2.948 or Accredited for FCC work. Search
under “Test Firms”. Then search by the level of accreditation needed.
Source: FCC FAQ's