I did not find a border option. As a workaround, you could plot the points twice. The first time with black shapes and the second time with slightly smaller shapes of the colour you want.
unset key
set xrange [0.6:3.4]
set yrange [0:3]
# Square
set style line 1 linecolor rgb '#000000' pointtype 5 pointsize 3
set style line 2 linecolor rgb '#ebac23' pointtype 5 pointsize 2
# Circle
set style line 3 linecolor rgb '#000000' pointtype 7 pointsize 3
set style line 4 linecolor rgb '#ebac23' pointtype 7 pointsize 2
# Triangle
set style line 5 linecolor rgb '#000000' pointtype 9 pointsize 3
set style line 6 linecolor rgb '#ebac23' pointtype 9 pointsize 2
plot "<echo '1 2'" with points ls 1, \
"" with points ls 2, \
"<echo '2 1'" with points ls 3, \
"" with points ls 4, \
"<echo '3 1.5'" with points ls 5, \
"" with points ls 6

Unfortunately, the triangle doesn't look quite right. It seems the centre of the two triangles are not perfectly aligned. Still, maybe this is good enough. If not, you could try the diamond or pentagon shapes since they both look better.