Not sure if I understand you correctly. From your sample code I take: You want to print on row 2, then put the cursor on the beginning of the very same row and get the user input until EOL? In any case, I'd recommend to use Term::Screen::ReadLine, not Term::Screen. If I understood you right, I guess it should be along the lines of the following:
#!/usr/bin/perl
use strict;
use Term::Screen::ReadLine;
my $t = Term::Screen::ReadLine->new;
$t->clrscr;
#$t->at(2, 0)->puts("this is some stuff");
my $in = $t->readline(ROW => 2, COL => 0, OVERWRITE => 0, LINE => "this is some stuff");
$t->at(3, 0)->puts("You wrote '$in'");