What is the deadline to put money in 2019 IRA

It sounds like you are describing a "backdoor Roth IRA contribution", where you make a non-deductible Traditional IRA contribution, and then convert it to a Roth IRA. Assuming you have no pre-tax money in Traditional IRAs, this process does not incur any taxes, and thus is effectively the same as a regular Roth IRA contribution.

The answer is that you can still do this up to July 15, 2020. Or more specifically, the deadline for the first step, the Traditional IRA contribution, is July 15, 2020, and it doesn't matter when you do the second step (the conversion to Roth IRA). Yes, it is true that the Roth IRA contribution will count under the year when the conversion was made, so even if you do the conversion between January 1, 2020 and July 15, 2020, it will count as a 2020 conversion. But it doesn't really matter what year the conversion counts under, since under a properly-executed backdoor Roth IRA contribution, the conversion step incurs no tax anyway. The only thing that that would be different when you do the conversion in 2020 vs 2019 is that you will report it on your 2020 Form 8606 instead of on your 2019 one.

The reason that the contribution has to be made before April 15 and counted under 2019 is that the year of contribution matters for the annual IRA contribution limit of $6000. However, there is no annual limit on conversions, so that consideration doesn't apply to the conversion step.