After specifying a padding mode, it works:

$rsa->use_pkcs1_padding;

my $buf = 't';
my $cipher = $rsa->encrypt($buf);

my $plain = $rsa->decrypt($cipher);
print "$plain\n";
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Update:

The linked article suggests "no padding". In that case we need a buffer of exact the size of the modulus, i.e. 319 bit. This is weird, as 39 byte are too short and 40 byte are too long. Prepending some bits (e.g. 0x1) in front of the data and filling the buffer to a total length of 40 byte does the trick:

$rsa->use_no_padding;

my $in = join '', 'a' .. 'z';
my $buf = pack 'Ca39', 0x1, $in;
my $cipher = $rsa->encrypt($buf);

my $plain = $rsa->decrypt($cipher);
print unpack 'xZ39', $plain;
[download]

Update 2:

When custom padding ("no padding") is in effect, the buffer must be the same size as the modulus and the to-be-encrypted value must be less than the modulus. So here we need a buffer of 40 byte. The modulus starts with 0x51. If the first byte of the to-be-encrypted value is less than 0x51 then the remaining 39 bytes may be arbitrary.