Many experiments, requiring dilute sulphuric acid, also can be done with NaHSO4 (so-called pH-minus from swimming pool / spa suppliers).
Making sulphuric acid can be done fairly easily by leading SO2-gas through a solution of H2O2:
SO2 + H2O2 ---> H2SO4.
A decent source of SO2 is mixing NaHSO4 with Na2S2O5 or K2S2O5 (sodium/potassium metabisulfite, available from shops for breweries/wine makers, as disinfectant or anti-oxidant), adding a few drops of water, and gently heating. You will get quite a lot of SO2 in this way, and you can lead that through the H2O2.
A solution of 3% H2O2 will lead to approximately 10% H2SO4. Try to find a somewhat more concentrated solution of H2O2.
But still, making H2SO4 at home from other reagents is a difficult thing. The H2O2/SO2 route is a moderately practical one, but still it is a lot of hassle, especially if you need to use 3% H2O2. H2SO4 actually is one of those chems that you don't want to make, but should put more effort in finding a source for this.
It is used in some drain cleaners at 90+ % concentration.
It is used in car batteries. Battery acid has 30 to 35% concentration.