I would use "could".
I asked my sister to call me on skype so I could be there for our mom's 60th birthday party.
I say on my mom's birthday: I asked Michelle to set it up so I could/can be here with you mom!
Are both okay here?
Why would you use could?
... so I could be here with you, Mom.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
These days, most people don't bother with "call me on Skype". Skype has become an accepted verb.
I asked my sister to Skype me ...
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.