How many times in a year can you do a 401k to Roth 401k conversion ?

There are no limits for trustee to trustee transfers/conversions  other than what the 401K plan administrator may impose.  Be careful on what you are trying to do ... a 401K rolls to a Traditional IRA and a roth 401K rolls to a Roth IRA.  Moving from a 401K to a roth IRA directly is a taxable conversion.  

Although there are no statutory limits, the 401(k) plans might have limitations on how often you can make distributions, so check with the plans for any such plan limitations.

Note that such "conversions" to a Roth 401(k) must be done in-plan.  You are not permitted to move funds from a traditional 401(k) account in one plan directly to a Roth 401(k) account in a different plan.