Platforms to make online experiments with counterbalancing
You could try www.gorilla.sc  It's cloud based software specifically designed for running cognitive psychology experiments online without needing to code.  It's not free, but it is affordable - £0.75 per participant.

Counterbalancing of various sorts is built in; randomisers, stimuli set counterbalancers, order counterbalancers.  It sounds like the simple randomiser set to balanced will do what you want.  As long as you stay on top of rejecting Ns that drop out, you'll get a balance in each condition.

There is a GUI questionnaire builder, task builder and experiment tree builder.  So you don't need to do any coding.  The vast majority of cognitive science task can be created in it very easily.

Full disclosure, I created Gorilla.