Your Oil Palm has leaf spot. This is a general term for a condition that can have many causes.
The disease can be caused by Fungi, Water Moulds and in one case a bacteria
Acidovorax, Annellophora, Bipolaris, Botrytis, Cylindrocladium (=Calonectria), Cercospora, Colletotrichum, Exserohilum, Gliocladium, Pestalotia, Pestalotiopsis, Phaeotrichoconis, Phytophthora, Pseudocerspora, Stigminaitalic
Acidovorax belongs to the Kingdom Bacteria. Phytophthora belongs to the Kingdom Stramenopila. The remaining pathogens belong to the Kingdom Fungi.
The condition, leaf spot is found throughout the world. It is possible that in your area only a few of teh agents cause the disease.
It is really important to stress that you cannot decide on what is causing this without a closer examination with a microscope.
Here is some text from an excellent resource (which is in the public domain and which I credit below)
"Despite the many pathogens that cause leaf spots and leaf blights, the initial symptoms are very similar.
Initial leaf spots are usually round to oval in shape and vary in color from yellow to brown to black. The initial size may be as small as a pin point. Some leaf spots initially appear as water-soaked lesions (Fig. 1). At some point during disease development, leaf spots will have a contrasting colored edge or halo - e.g., brown spot with a yellow halo, tan center with brown edge or gray center with black edge and a yellow halo (Figs. 2-4). All color combinations are possible. As the leaf spots expand in size, the shape and coloration may change (Fig. 5). As the disease progresses, leaf spots often coalesce (merge together) to form large areas of blighted tissue (Fig. 1), hence, the term leaf blight. If the disease continues to develop, leaflets or the entire leaf may die prematurely.
Any age leaf can be affected by leaf spots, and there usually is no distinct pattern to the spotting . Leaf spot diseases may occur at any stage of palm growth, but are a more serious problem of seedling and juvenile palms because they have fewer number of leaves or the leaves are smaller in size than in a mature palm.
One should not guess as to the identity of the pathogen based on the leaf spot symptom observed. Identification is based on observation of the pathogen spores, either directly on the leaf tissue (Fig. 6) or in culture after isolating from the leaf tissue".
Broschat, T. K., M.L. Elliott, I. Maguire. 2010. Symptoms of Diseases and Disorders. In A Resource for Pests and Diseases of Cultivated Palms. University of Florida, Identification Technology Program, CPHST, PPQ, APHIS, USDA; Fort Collins, CO. [April 6th 2014]
One of the authors of the above text, Dr Monica Elliot wrote this about control in Nurseries
"In a nursery situation, severely diseased leaves should be pruned and destroyed to reduce spores available to infect healthy tissue. If the palm is small with only a few leaves, eliminate the palm completely."
She was speaking about Pestalotiopsis diseases (Fungus) but it would apply to all the fungal/water mold described above as watering and humid conditions promote their spread.
And also here
"While fungicides may be useful to prevent further spread of the disease, they are merely a supplement to water management, sanitation, injury prevention and good palm nutrition. Fungicides alone will not solve the problem. It is critical to understand that fungicides do not cure the leaf spot or petiole blight already present. Once a leaf spot or petiole lesion occurs, it will remain for the duration of the life of that leaf. Fungicides are used to prevent further spread of the disease by protecting leaf tissue that has not been infected by the fungal pathogen.
In the nursery situation, prune severely diseased leaves prior to fungicide application. These leaves need to be removed anyway, and this will reduce the amount of fungicide used in the process. In the landscape situation, unless the leaf spot disease is severe, leaf pruning is not recommended unless the palm is free of nutrient deficiencies. In general, nutrient deficiencies are far more debilitating to the landscape palm than leaf spot diseases."
Questions for you
Please can you send images of the surrounding plants?
Do you have many insects (damage by insects spreads disease)
Do you water from above? (It is best to water directly onto the ground, at the base)
What time of day do you water?
Figure 1 (from quoted text). The initial lesions of this leaf spot disease are pin point water-soaked appearing spots. As the spot expands, the center becomes gray with water-soaked edges As the lesions continue to expand, a yellow halo may be observed. Coalescing of expanding lesions are observed until large areas of blighted tissue result.
Figure 4. A leaf affected by both Graphiola leaf spot and Stigmina leaf spot. Signs of Graphiola phoenicis are the small back bodies (sori), many with filaments emerging from the sori. Stigmina palmivora symptoms are the large brown spots with dark edges and darker but flat centers. In some cases, a G. phoenicis sorus is superimposed upon the S. palmivora leaf spot.
Figure 2. Leaf spot exhibitng brown or black centers with yellow halos. Spots are randomly scattered on the leaf tissue. Photo by T. K. Broschat.
Figure 5. Spots are initially black with no halos. As the spot expands, the center becomes tan and is outlined by a brown to brownish-black edge, but no yellow halo. The leaflet in the lower-left corner has large areas of necrotic tissue. The leaf spot is superimposed on iron deficiency symptoms. Photo by M. L. Elliott.
Figure 3. Leaf spot that begins as a black spot with distinct yellow halo. As the lesion expands or lesions coalesce, the affected area becomes a leaf blight and the center becomes a gray color.
Figure 6. A leaf spot symptomatic leaf segment of the leaf in Figure 1 was placed under high humidity. The result was growth of the fungus from some of the spots. Note fungal growth is only associated with the leaf spot symptom and not with the healthy green leaf tissue. Photo by M. L. Elliott.