What kinds of tools do you have?
What I would do is this. Measure a diameter. This you can do precisely (like with a micrometer or good caliper). Take a steel plate with flat side (think about a ruler if the cylinder's diameter is small enough). Clamp a C clamp with a round leg to it so that the distance from the edge of the plate, to the point of the leg nearest to the edge, is exactly half the diameter. Again, a caliper would be your great friend.
Now you have a tool for drawing diameters on the circular side of the cylinder. All you have to to is put the flat piece on the face of the cylinder, so that the leg of the C clamp touches the side of the cylinder, and draw a line with a hard needle of some sort. That would be a diameter of the circle. Draw another diameter at close to 90 degree angle to the old diameter (exactly 90 degrees is not necessary). The point of the intersection of the two diameters is the center.
You may be fine with the approximation that the intersection is the center.
If not...
If you draw four of such diameters, they would, in the real world, due to measurement errors, define not one point, but a tiny quadrangle, vanishingly small. Its center is the true center.
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