If I am writing a CV, is it correct to use past continuous tense as follows:
From 2011 to 2012, I was doing some part-time design jobs.
Thanks.
That doesn't sound appropriate to me. In CVs, we sometimes don't even use whole sentences:
2011-2012: Various part-time design jobs.
Depending on the CV and the jobs you are applying for, you might need to list those part-time jobs (location, job description, name of manager etc).
I prefer the past tense there too. You could also say:
I worked part-time in several different design jobs in 2011 and 2012.