My own method would be as follows (although it would be a bit easier to do if I knew what volumes of your final solutions you wanted). Anyway...
For the 1mM -- 50pM dilution, calculate that 1mM = 1,000,000,000pM. I'm not using standard form as it looks untidy on this. Anyway, you're therefore doing a 1 in 20,000,000 dilution. I've always been told that pippetting minute volumes isn't as accurate as adding extra steps, and also the exact way I'd do this depends on how much final volume you want. However, a suggestion is...
First, make up 10ul of your original 1mM solution to 100ml (in water, buffer, or whatever else you use), a 1 in 10,000 dilution, giving you a new conc of 100nM solution.
Then, take 50ul of this second solution, and make up to 100ml with your water/buffer/etc, a 1 in 2,000 dilution. You will then have a 100ml solution of concentration of 50pM (a final dilution from the original of 1 in (10,000 x 2,000) = 1 in 20,000,000.