2 added 405 characters in body
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according to thisHasidicUniversity.org, (who lists what are obligation privileges (to do mitzvot) non-Jew's are) hea non-Jew may countdo the mitzvah of counting the omer
see(Related Rambam Kings 10.10
Where the Rambam says non-Jew's are alowed to do mitvot)

but without a blessing
(see Rambam Blessings 11.7 Where the Rambam seems to hint (at least that is how HasidicUniversity.org seems to understand him) that a non-jew should not make blessing of mitzvot)

(In this case Hasidic is from the words hasidai umot haolam)

according to this, he may count
see Rambam Kings 10.10

but without a blessing
see Rambam Blessings 11.7

according to HasidicUniversity.org (who lists what are obligation privileges (to do mitzvot) non-Jew's are) a non-Jew may do the mitzvah of counting the omer
(Related Rambam Kings 10.10
Where the Rambam says non-Jew's are alowed to do mitvot)

but without a blessing
(see Rambam Blessings 11.7 Where the Rambam seems to hint (at least that is how HasidicUniversity.org seems to understand him) that a non-jew should not make blessing of mitzvot)

(In this case Hasidic is from the words hasidai umot haolam)

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according to this, he may count
see Rambam Kings 10.10

but without a blessing
see Rambam Blessings 11.7