If you have a function generator which can output a staircase function, you could do a quick test with the scope in XY mode. The frequency should be set such that each step lasts for 200 ns; the number of steps does not really matter. My Siglent SDG2042 has a predefined function with 8 or 10 equidistant steps up, then dropping all the way back down, which works nicely.
If you put the scope into XY mode and feed the staircase signal to the Y axis, you should see a vertical column of nicely defined dots. (The Y axis will definitely have enough bandwidth.) If you connect the signal to the X axis instead and the dots still look OK, then the scope is fine for this job! My old Hitachi shows very blurry dots in the X direction, and gets completely messed up by the large step back down at the end of the scan line.
OK, I see how you are doing this. If you have 200ns dwell time and you want the trace to move quickly to the next one, a scope with a maximum sweep rate of 50ns/div
may will not have enough horizontal amplifier bandwidth. A scope with a 5ns/div or 10ns/div sweep rate might be better, but unless you blank the trace during the movement, you'll still see the lines between the dots. If you are representing the data by having the dot there or not, are you doing this with Z-blanking or by skipping that step in the trace?
I tried what you are attempting with a Tek 2445, which is certainly at the high end of 'cheap analog scopes'. It has a 10ns/div max sweep rate without magnification and a rated X bandwidth of 3MHz. I used an 8-step stair repeated at 625kHz, for 200ns steps as shown. It works, but not very well--there is a line between the dots. The picture is worse than the reality, the dots are clearly visible, but the line is there. This scope has the ability to select the Y channel in XY mode, and you can select the same as X/CH1 for an 'XX' mode. You might think this could only yield a diagonal line, but the bandwidth difference between the horizontal amp and vertical amp actually gives you interesting information. One problem is that your 200ns-per-step stair has a fundamental bandwidth of 5MHz but like representing a square wave, you will need 5-10X that in bandwidth to have a sharp, crisp move from one dot to the next. The other issue is that the visibility of the trace is quite non-linear, so even if the trace spends 99% of the time at the dots and 1% in between, you still see the line quite clearly.
Lowering the frequency to 62.5kHz w/ 2us steps gave brighter dots with a dimmer line, but still not perfect. 6.25kHz w/ 20us steps gave nice clear dots with no visible lines and the retrace in XX mode was only slightly visible at the highest intensity. The 2445 is visibly out of phase in XX mode with a 3 MHz sine wave input. Since any scope with a delay line is likely to have its X-bandwidth limited to prevent an erroneous out-of-phase display, what you are doing is going to be tough with any ordinary scope. I assume each scan line will be a row of data and then you will step more slowly the other way to display multiple rows in a matrix. Can you scan the other way, so as to use the Y-axis' greater bandwidth? I tried it and got a clear matrix, but still with a visible line between the dots.