I had the same issue when I was training. I talked to friends and instructors and devised the following to help me:
1. Trim the aircraft so it flies 'hands off'. Probably hard in the school's 152 that's had more bounces than your average space hopper, but get it as good as possible. Trimming accurately is essential for this exercise.
2. Hold the chart up as far as you can. Using a small kneeboard or clipboard gave me something to lean against. This way the horizon stays in your peripheral vision and you can detect any roll more easily and be quicker to correct it. Also reminds you to do a thorough LOOKOUT
3. Get the right tools and do the right preparation. On my marker pen for my chart I wrapped it in a length of white tape and marked on lines for 5nm, 10nm, 15nm etc. This made it really easy to measure, mark off and calculate my timings. I also had a small credit card sized straight edge that was around my neck, perhaps you have an air side pass/ID badge that might suffice? For the prep; my school taught the 'Max drift' and 'clock code' method of working out headings. I always had the Max drift, wind vector and clock code marked on my chart somewhere (usually out to sea).
4. CHUNK. Do one task at a time, for example: Circle your diversion point, fly the aircraft, circle the diversion destination, fly the aircraft, draw the line, fly the aircraft, estimate true heading, fly the aircraft etc etc, you get the picture.
Diverting using map and compass is as much an exercise in workload management as it is in map skills etc, so make it as easy as possible for yourself. When they ask you to plan a diversion don't think you must go immediately, manage your workload by going from the next sensible point such as your next "feature" (My school called them 'event cycle features'). Other posts have talked about holding over a known point, but i'd say this is false economy as you are increasing your workload and also you are likely to be drifted away from your planned track, further adding to your workload.
If you do need to turn immediately on a diversion track then use the "big to small" method; decide where you need to go and turn towards it as best as you can using big features such as towns, cities the coast and of course the sun. This is somewhat harder as you need to still do all the same tasks for diverting while also planning the diversion. However once planned you can parallel your diversion track and then regain it. (This is also where local knowledge comes in, have a look at all the airfields around your route and get a rough idea of where they are in relation to the big features in the area, possibly have in mind a rough direction to turn in for the likely diversions you will get)
I found that learning to do this well really set me up for instrument flying, as that is also all about managing your workload and being methodical in your scan. Good luck in the rest of your training.