The plan seems relatively simple then. Although maybe not very well thought out would be the better word.
With only 63 mercenaries and apparently no domestic support there's really only one thing they can do. Assault the presidential palace or whatever residence the president is at, and take him hostage, along with other governmental officials.
Thats dicey enough. 63 mercenaries, plus whatever local contacts they have (thats assuming they do have some) need to take on the presidential guard, police, and any local army units. After that they'll need to survive. They could potentially have some safehouses to flee to, or just try to escape the capital out right, but the most likely plan is to try to hold the presidential palace in a siege. That assumes they successfully capture it.
If they manage to capture the palace, then they could potentially survive. The morale of Guinean army isnt something to write home about, and their troops could potentially be reluctant to storm a building manned by foreign troops with decent training, marksmanship and heavy firepower. Taking hostages also increases their survival chance, particularly if the hostages are government officials, or the president himself.
From there things get even more dicey. The mercenaries have their standoff in the capital, with the president ether dead or a hostage. Now the focus shifts to the guy the mercenaries were planning to put into power, and the people backing him. He could try doing a public broadcast annoucing regime change and hoping it leads to a popular revolution by the people, and hoping it causes elements of the army to defect to his cause. That could potentially be 'helped along' by entering negotiations with the military and police commanders and seeing if they could be persuaded with some financial incentives to defect. All of Equatorial Guinea's generals are relatives of Obiang though, which makes it difficult. Many promises are going to need to be made.
If elements of the army defect to the coup, then potentially it could succeed and Severo Moto would enter the nation as president and take control.
Lots of ifs though, and it seems a bit farfetched. But thats how i see it playing out.
Now the Spanish are another if factor. If they really are on the side of the coup, it depends on how blatant they are willing to be. If they commit totally, their 500 Spanish marines could take control of most of the capital out right. Which greatly increases the position of the coup.
It requires the Spanish to be totally committed though, since that is rather risky and public for the Spanish government.
And of course the safest place for Mr. Severo Moto to be would be onboard those Spanish warships.