You are really pushing the limit as to what the system was designed to do. It is NOT resonable to dispense 0.1 ul volumes with high accuracy using that type of system.
Some Comments/Suggestions:
1) Can you use a larger volume column ? That would enable you to inject a larger volume of sample onto the column.
2) The standard loop can be replaced with a lower volume capillary (only if you NEVER inject volumes greater than about 80ul). This would decrease some diffusion effects as the autosampler's pump (one half of an 1100 pump head which is a 100 ul variable volume/stroke piston) is aspirating the sample. *Would it really help in this case. Probably not since you are working at the very bottom of what is the acceptable range of the 0.1 to 100 ul system. Just wanted you to know that it can be done.
3) Do the dilution in TWO steps to keep the final volume small (5 ul in your case), but put the injector back into a range where it can show some accuracy in the draw and dispense positions plus give you a chance at having a good reproducibilty number. This is why programmable autosamplers/autoinjectors exist. They can be used as sample preparation stations.
Example #1: Program the A/I to draw up 490 ul of diluent and then dispense it into a new vial, we will call it vial # 2 (this can be done in steps, 100 ul at a time). Next program the system to aspirate 10 ul of your sample from the designated "Sample" vial and then dispense it into Vial #2. That should give you 500 ul of a 50:1 solution with both values within the range of the A/I.
Example # 2: Program the A/I to draw up 245 ul of diluent and then dispense it into a new vial, we will call it vial # 2 (this can be done in steps, 100 ul at a time). Next program the system to aspirate 5 ul of your sample from the designated "Sample" vial and then dispense it into Vial #2. That should give you 250 ul of a 50:1 solution with both values within the range of the A/I.
Mix and match values in two, three or however many steps to get whatever ratio you need. You may also want to use the aspirate and dispense functions of the needle/loop ('Swish' mode) to mix the final solution in vial #2 before you draw your actual sample.
4) Injection speed matters when viscosity is an issue. No idea what if any viscosity issues you have.
5) Try any of the above and repeat the test about ten times to get some idea of the injection reproducibility. If none of these ideas works in your situation, then consider manually preparing solutions, using a nano-injector or changing the method.