Today (Sunday), it will be mostly cloudy/rainy BUT you might be able to say between 10 pm and midnight.
Monday night (the night of ט’ שבט) will be partly cloudy. You should be able to see the לבנה from 6 PM until 12 midnight. (But will be going in-and-out of clouds.)
Tuesday night (the night of י’ שבט) looks to be cloudy. You might be able to see the moon around 7 pm.
Wed night and Thurs night looks to be rainy all night.
Friday night looks to be mostly clear starting around 6:30 pm. (NOTE: Since Friday night is the next-to-last night many hold that you can say it, even though normally you would not. Ask your Rov if you should.)
מוצאי ש”ק פ’ בשלח is the LAST night to say קידוש לבנה this month. According to the רמ”א it should be said by 7:47 pm. According to the מחבר you can say it until 1:25 AM. As of now it looks like you would be able to see the לבנה then.
You may have have to subtract approx 21 minutes from the 7 47 pm to adjust from Jerusalem solar time that the molad is in to Jerusalem standard time that we use . Please look into it and confirm if correct.
7:47 pm is correct and takes into account the 21 minute “deduction”.