The pygmt.Figure.plot method can plot points. The plot symbol and size is set with the style parameter.

import numpy as np
import pygmt

# Generate a random set of points to plot
rng = np.random.default_rng(seed=42)
region = [150, 240, -10, 60]
x = rng.uniform(low=region[0], high=region[1], size=100)
y = rng.uniform(low=region[2], high=region[3], size=100)

fig = pygmt.Figure()
# Create a 15 cm x 15 cm basemap with a Cartesian projection (X) using the
# data region
fig.basemap(region=region, projection="X15c", frame=True)
# Plot using inverted triangles (i) of 0.5 cm size
fig.plot(x=x, y=y, style="i0.5c", fill="black")

Total running time of the script: (0 minutes 0.162 seconds)

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