I planning a DONEX as follows:
MIA-LAX-SYD-HKG-DXB-CPT-LHR-DUB-MIA
but can't find a way to get from DXB to CPT.

Any suggestions?

I might be wrong. But, DXB is in Europe as per Continent. your routing is NA-PA-AS-EU-AF-EU-NA...Is that illegle? I think you would have no problem with:
1>, MIA-LAX-SYD-HKG-CPT (via Johanesburg)-DXB (via LHR/MAD?)-LHR-DUB-MIA
or
2>, MIA-LAX-SYD-HKG-DXB-DUB-CPT-MIA (via LHR).

Correct me if I am wrong.

IC6A's (1) is mostly correct; (2) is incorrect.

DXB is counted as Europe, so by entering Europe once (from HKG) you can't re-enter it a second time (from CPT.) There are exceptions in Africa from which you're allowed a second entry into Europe (e.g. NBO, DAR, ACC) because there are no other continents served from those airports, but South Africa is not on that list.

The "legal" routing would be ...HKG-JNB-CPT-LHR-DXB..

A couple of other routing issues: As of now there's no Oneworld service between the UK and DUB. All of BA's flights to Ireland are now codeshares using Aer Lingus metal, ineligible for use with xONExs. AFAIK the only Oneworld service into DUB from/to Europe is now IB's service from MAD.

A route that would comply with the rules for the OP would be something like MIA-LAX-SYD-HKG-JNB-CPT-LHR-DXB-LHR-MAD-DUB-ORD-MIA (or ...DXB-AMM-MAD-DUB... )

You still have 2 entries to EUR in your 2nd option. Even though the 2nd entry is a xfer it is not from one of the permitted countries.

Do you need to go to HKG?
If not you could do:
MIA-LAX-SYD-JNB-CPT-LHR-DXB-LHR-DUB-LHR-MIA
If HKG is necessary then:
MIA-LAX-SYD-HKG-DXB-LHR-DUB-LHR-CPT-SYD-ground-NBO-(xLHR)-MIA

Thanks to all.

I validated option 1 from IC6A. Next I'm on the hunt for the proper class seats.